POWER SYSTEM-I

Why is ACSR conductor used in overhead transmission line?

Define skin effect.

Draw the single-line diagram of typical power system.

Define critical disruptive voltage.

The insulation resistance of a single-core cable is 160 $ M\Omega/km $. What is the insulation for 4 km length of cable in $ M\Omega $?

What do you mean by Ferranti effect?

What is self-GMD?

Explain string chart. Why is it used?

What is the need of transposition of transmission lines?

Differentiate between ring feeder system and radial distribution system.

Derive the expression of inductance of a 3-phase transposed transmission line. Also calculate the inductance of equilateral triangular and horizontal configuration.

What are the different types of insulators in transmission system for overhead line? Explain them with suitable diagram.

A string of three insulators is connected across a 100 kV line. If the capacitance of each disc to earth is 0.1 of the capacitance of the insulator, calculate (i) the distribution of voltage on the insulator discs and (ii) the string efficiency.

What is a sag in overhead lines? Deduce an approximate expression for sag in overhead lines when (i) supports are at equal levels and (ii) supports are at unequal levels.

Explain the term 'surge impedance loading' (SIL).

A surge of 20 kV magnitude travel along a lossless cable toward its junction with two identical lossless overhead transmission lines. The inductance and capacitance of the cable are 0.4 mH and 0.5 $ \mu F $ per km. The inductance and capacitance of the transmission line are 1.5 mH and 0.015 $ \mu F $ per km. Find the magnitude of the voltage at the junction due to surge.

Explain corona and its effects on performance of transmission line. How can it be reduced?

A 3-phase line has conductors 2 cm in diameter spaced equilaterally 1 m apart. If the dielectric strength of air is 30 kV (max) per cm, find the disruptive critical voltage for the line. Take, air density factor $ \delta = 0.952 $ and irregularity factor $ m_0 = 0.9 $.

What are the different components of underground cable?

Why is grading required in underground cables? Explain different methods of cable grading.

What is neutral grounding? Describe different methods of neutral grounding and their advantages and disadvantages.

A transmission line conductor at a river crossing is supported from two towers at heights of 30 m and 90 m above water level. The horizontal distance between the towers is 270 m. If the tension in the conductor is 1800 kgf and the conductor weighs 1.0 kgf per metre, find the clearance between the conductor and the water at a point midway between the towers. Assume parabolic configuration.

Why is ACSR conductor used in overhead transmission line?

Define skin effect.

Draw the single-line diagram of typical power system.

Define critical disruptive voltage.

The insulation resistance of a single-core cable is 160 $ M\Omega/km $. What is the insulation for 4 km length of cable in $ M\Omega $?

What do you mean by Ferranti effect?

What is self-GMD?

Explain string chart. Why is it used?

What is the need of transposition of transmission lines?

Differentiate between ring feeder system and radial distribution system.

Derive the expression of inductance of a 3-phase transposed transmission line. Also calculate the inductance of equilateral triangular and horizontal configuration.

What are the different types of insulators in transmission system for overhead line? Explain them with suitable diagram.

A string of three insulators is connected across a 100 kV line. If the capacitance of each disc to earth is 0.1 of the capacitance of the insulator, calculate (i) the distribution of voltage on the insulator discs and (ii) the string efficiency.

What is a sag in overhead lines? Deduce an approximate expression for sag in overhead lines when (i) supports are at equal levels and (ii) supports are at unequal levels.

Explain the term 'surge impedance loading' (SIL).

A surge of 20 kV magnitude travel along a lossless cable toward its junction with two identical lossless overhead transmission lines. The inductance and capacitance of the cable are 0.4 mH and 0.5 $ \mu F $ per km. The inductance and capacitance of the transmission line are 1.5 mH and 0.015 $ \mu F $ per km. Find the magnitude of the voltage at the junction due to surge.

Explain corona and its effects on performance of transmission line. How can it be reduced?

A 3-phase line has conductors 2 cm in diameter spaced equilaterally 1 m apart. If the dielectric strength of air is 30 kV (max) per cm, find the disruptive critical voltage for the line. Take, air density factor $ \delta = 0.952 $ and irregularity factor $ m_0 = 0.9 $.

What are the different components of underground cable?

Why is grading required in underground cables? Explain different methods of cable grading.

What is neutral grounding? Describe different methods of neutral grounding and their advantages and disadvantages.

A transmission line conductor at a river crossing is supported from two towers at heights of 30 m and 90 m above water level. The horizontal distance between the towers is 270 m. If the tension in the conductor is 1800 kgf and the conductor weighs 1.0 kgf per metre, find the clearance between the conductor and the water at a point midway between the towers. Assume parabolic configuration.

Which of the following distribution systems is preferred for good efficiency and high economy?

The main drawback(s) of overhead system over underground system is/are

The highest transmission voltage used in India is

The function of steel wire in an ACSR conductor is to

Corona is accompanied by

The conductor carries more current on the surface in comparison to its core. This phenomenon is called the

Ferranti effect happens in transmission line when the line is

A transmission line is distortionless if

The receiving-end voltage of a transmission line will be greater than the sending-end voltage if the load is

Capacitor grading of cable means

Explain 3-phase, 4-wire system of distribution of electrical power.

A 2-wire feeder ABC has a load of 100 Ampere at unity p.f. at C and 65 Ampere at p.f. 0.8 lagging at B. The impedance AB is $ (0.06+j0.08)\Omega $ and that of BC is $ (0.04+j0.12)\Omega $. If the voltage at the far end C is to be maintained at 230 V, determine the voltage (i) at A and (ii) at B.

Derive an expression for the capacitance of a single-phase overhead transmission line.

Find out capacitance of a single-phase line 30 km long consisting of two parallel wires each 15 mm diameter and 1.5 m apart.

A single-phase line has an impedance of $ 5 \angle 60^{\circ} \Omega $. It is supplying a load of 120 A, 33 kV at 0.8 p.f. lagging. Calculate its regulation.

In a 3-phase, 4-wire system, the line voltage is 400 V and non-inductive loads of 10, 8 and 5 kW are connected between the three line conductors and the neutral. Calculate (i) the current in each line and (ii) the current in the neutral conductor.

What are the sources of vibrations in a transmission line? Explain the methods used to damp out these vibrations.

Obtain an expression for the sag of a transmission line supported by towers of different heights at the ends.

Define regulation of a 3-phase a.c. transmission system and develop an expression for approximate voltage regulation.

Explain surge impedance loading with respect to an overhead transmission line.

An overhead 3-phase transmission line delivers 5 MW at 22 kV at 0.8 lagging power factor. The resistance and reactance of each conductor are 4 $ \Omega $ and 6 $ \Omega $ respectively. Determine: (a) Sending-end voltage (b) Percentage regulation (c) Total line losses (d) Transmission efficiency.

With the neat labelled diagram, show the various parts of a high-voltage single-core cable.

Explain briefly the following methods of grading of cables: (i) Capacitance grading (ii) Intersheath grading.

A 132 kV transmission line has the following data: Weight of conductor = 680 kg/km, Length of span = 260 m, Ultimate strength = 3100 kg, Safety factor = 2. Calculate the height above ground at which the conductor should be supported. Ground clearance required is 10 m.

The three conductors of a 3-phase transmission line are arranged in a horizontal plane and are 3 m apart. The diameter of each conductor is 4 cm. Determine the inductance per km of each phase. Assume balanced load and R, Y, B phase sequence.

Which of the following distribution systems is preferred for good efficiency and high economy?

The main drawback(s) of overhead system over underground system is/are

The highest transmission voltage used in India is

The function of steel wire in an ACSR conductor is to

Corona is accompanied by

The conductor carries more current on the surface in comparison to its core. This phenomenon is called the

Ferranti effect happens in transmission line when the line is

A transmission line is distortionless if

The receiving-end voltage of a transmission line will be greater than the sending-end voltage if the load is

Capacitor grading of cable means

Explain 3-phase, 4-wire system of distribution of electrical power.

A 2-wire feeder ABC has a load of 100 Ampere at unity p.f. at C and 65 Ampere at p.f. 0.8 lagging at B. The impedance AB is $ (0.06+j0.08)\Omega $ and that of BC is $ (0.04+j0.12)\Omega $. If the voltage at the far end C is to be maintained at 230 V, determine the voltage (i) at A and (ii) at B.

Derive an expression for the capacitance of a single-phase overhead transmission line.

Find out capacitance of a single-phase line 30 km long consisting of two parallel wires each 15 mm diameter and 1.5 m apart.

A single-phase line has an impedance of $ 5 \angle 60^{\circ} \Omega $. It is supplying a load of 120 A, 33 kV at 0.8 p.f. lagging. Calculate its regulation.

In a 3-phase, 4-wire system, the line voltage is 400 V and non-inductive loads of 10, 8 and 5 kW are connected between the three line conductors and the neutral. Calculate (i) the current in each line and (ii) the current in the neutral conductor.

What are the sources of vibrations in a transmission line? Explain the methods used to damp out these vibrations.

Obtain an expression for the sag of a transmission line supported by towers of different heights at the ends.

Define regulation of a 3-phase a.c. transmission system and develop an expression for approximate voltage regulation.

Explain surge impedance loading with respect to an overhead transmission line.

An overhead 3-phase transmission line delivers 5 MW at 22 kV at 0.8 lagging power factor. The resistance and reactance of each conductor are 4 $ \Omega $ and 6 $ \Omega $ respectively. Determine: (a) Sending-end voltage (b) Percentage regulation (c) Total line losses (d) Transmission efficiency.

With the neat labelled diagram, show the various parts of a high-voltage single-core cable.

Explain briefly the following methods of grading of cables: (i) Capacitance grading (ii) Intersheath grading.

A 132 kV transmission line has the following data: Weight of conductor = 680 kg/km, Length of span = 260 m, Ultimate strength = 3100 kg, Safety factor = 2. Calculate the height above ground at which the conductor should be supported. Ground clearance required is 10 m.

The three conductors of a 3-phase transmission line are arranged in a horizontal plane and are 3 m apart. The diameter of each conductor is 4 cm. Determine the inductance per km of each phase. Assume balanced load and R, Y, B phase sequence.

The angle of A, constant of the transmission line normally lies between

By increasing the transmission voltage to double of its original value, the same power can be despatched keeping the line loss

Power transmission by cable is generally adopted for line lengths

Reactive power is

In a long transmission line under no-load condition

The presence of earth in case of overhead lines

The effect of bonding the cable is

Effect of increase in temperature in overhead line is to

The capacitance between any two conductors of a 3-core cable with sheath earthed is $ 3 \mu F $. The capacitance per phase will be

To obtain the minimum value of stress in cable R/r ratio should be

Compare the volume of copper required for the distributor cable in a low-voltage distribution network in a DC 3-wire system, with a 3-$\phi$, 4-wire system. Assume the same consumer voltage, same percentage loss, unity power factor and balanced load. The neutrals of half the X-section of corresponding outer.

Write a short note on 'choice of transmission voltage'.

A 2-core, 11 kV cable is to supply 1 MW at 0.8 p.f. lag for 3000 hours in a year. Capital cost of the cable is $ (20 + 400a) $ per meter, where a is the X-sectional area of core in $ cm^2 $. Interest and depreciation total 10% and cost per unit of energy is 15 P. If the length of cable is 1 km, calculate the most economical X-section of the conductor. The specific resistance of copper is 1.75 $ \mu\Omega-cm $.

A 1-$\phi$ distributor, one km long has resistance and reactance 0.4 $ \Omega $ and 0.6 $ \Omega $ (go and return) respectively. At the far end, the voltage $ V_B = 240 $ V and the current is 100 A at a p.f. of 0.8 lag. At the mid-point B of the distributor current of 100 A is tapped at a power factor of 0.6 lag with reference to the voltage $ V_B $ at the mid-point. Calculate the supply voltage $ V_S $ for the distributor and the phase angle between supply end and receiving end.

Derive from first principles, the capacitance per km to neutral of a 3-$\phi$ overhead transmission line with unsymmetrical spacing of conductors assuming transposition.

Discuss the effect of wind and ice on sag.

What is a stringing chart? What is its utility?

Explain the physical significance of the generalized ABCD constants of a transmission line. State the units of these constants. Determine these constants for a medium transmission line with nominal-T configuration. Draw neatly corresponding vector diagram.

Explain in detail how the receiving end power circle diagram can be drawn. Obtain the condition for maximum power.

Find expression for the capacitance of a cable per km length.

Write a short note on thermal resistance of cables.

The angle of A, constant of the transmission line normally lies between

By increasing the transmission voltage to double of its original value, the same power can be despatched keeping the line loss

Power transmission by cable is generally adopted for line lengths

Reactive power is

In a long transmission line under no-load condition

The presence of earth in case of overhead lines

The effect of bonding the cable is

Effect of increase in temperature in overhead line is to

The capacitance between any two conductors of a 3-core cable with sheath earthed is $ 3 \mu F $. The capacitance per phase will be

To obtain the minimum value of stress in cable R/r ratio should be

Compare the volume of copper required for the distributor cable in a low-voltage distribution network in a DC 3-wire system, with a 3-$\phi$, 4-wire system. Assume the same consumer voltage, same percentage loss, unity power factor and balanced load. The neutrals of half the X-section of corresponding outer.

Write a short note on 'choice of transmission voltage'.

A 2-core, 11 kV cable is to supply 1 MW at 0.8 p.f. lag for 3000 hours in a year. Capital cost of the cable is $ (20 + 400a) $ per meter, where a is the X-sectional area of core in $ cm^2 $. Interest and depreciation total 10% and cost per unit of energy is 15 P. If the length of cable is 1 km, calculate the most economical X-section of the conductor. The specific resistance of copper is 1.75 $ \mu\Omega-cm $.

A 1-$\phi$ distributor, one km long has resistance and reactance 0.4 $ \Omega $ and 0.6 $ \Omega $ (go and return) respectively. At the far end, the voltage $ V_B = 240 $ V and the current is 100 A at a p.f. of 0.8 lag. At the mid-point B of the distributor current of 100 A is tapped at a power factor of 0.6 lag with reference to the voltage $ V_B $ at the mid-point. Calculate the supply voltage $ V_S $ for the distributor and the phase angle between supply end and receiving end.

Derive from first principles, the capacitance per km to neutral of a 3-$\phi$ overhead transmission line with unsymmetrical spacing of conductors assuming transposition.

Discuss the effect of wind and ice on sag.

What is a stringing chart? What is its utility?

Explain the physical significance of the generalized ABCD constants of a transmission line. State the units of these constants. Determine these constants for a medium transmission line with nominal-T configuration. Draw neatly corresponding vector diagram.

Explain in detail how the receiving end power circle diagram can be drawn. Obtain the condition for maximum power.

Find expression for the capacitance of a cable per km length.

Write a short note on thermal resistance of cables.

For a medium length transmission line, A is

To increase the transmission capability of a high-voltage longline

The surge impedance of 50-mile long underground cable is 50 ohms. For a length of 25 miles the impedance will be

In a transmission system, the weight of copper used is proportional to

Stringing chart is useful for

The regulation of a line at full-load 0.8 of lagging is 12%. The regulation at full-load 0.8 p.f. leading can be

The inductance of a line is minimum when

Which distribution system is more reliable?

In a 3-core cable, the capacitance between 2 conductors (with sheath earthed) is 3 $ \mu F $. The capacitance/phase is

For a transmission line with resistance R2, reactance X2 and negligible capacitance, the parameter A is

Describe the various systems of power transmission and compare the following as regard to the amount of copper used for the same distance, the same power transfer, the same maximum voltage to ground and the same power loss: (a) 3-phase, 3-wire AC (b) 3-wire DC (c) 1-phase, 2-wire AC.

State Kelvin's law and explain why in practice the law is usually not strictly observed.

The following data relate to a 2-wire feeder: Current carried throughout the year = 220 A. The portion of the capital cost which is proportional to X-sectional area = 6 per kg of Cu conductor. Cost of energy = 6 P per kWh. Interest and depreciation charges = 10% PA. Density of copper = 8.93 $ g/cm^3 $. Specific resistance of copper = 1.8 $ \mu\Omega-cm $. Find the most economical X-section of the conductor.

A 1.5 km long single-phase 2-wire feeder supplies the loads as under: 60 A at 0.8 p.f. (lagging), 600 m from the fed point. 40 A at 0.85 p.f. (lagging), 1200 m from the fed point. 50 A at 0.88 p.f. (lagging), 1500 m from the fed point. The resistance and reactance of the feeder per km length (go and return) are 0.1 $ \Omega $ and 0.2 $ \Omega $ respectively. If the voltage at the far end is to be maintained at 220 V, calculate the voltage of the sending end, and its phase angle with respect to the receiving end voltage.

Find the inductance per phase of 3-$\phi$ overhead transmission line using 2 cm diameter conductors when these are placed at the corners of equilateral triangle of sides 4 meters. Also do the derivation needful.

The three conductors of a 3-$\phi$ transmission line are arranged in a horizontal plane and are 4 meters apart. The diameter of each conductor is 2.5 cm. Determine the inductance per km of the each conductor (line to neutral). Assume balanced load and R, Y, B phase sequence. Determine the average inductance per phase for regularly transposed line.

Discuss the effect of wind and ice on sag.

The following data refers to a transmission line supported on level supports: Span length = 220 meters. Hard drawn copper conductor: X-sectional area = 120 $ mm^2 $, 37/2-11 mm; $ W_c = 1/2 $ kg/m. Ultimate tensile stress = 42.2 $ kg/mm^2 $. Factor of safety = 4. Wind pressure = 55 $ kg/m^2 $. Thickness of ice coating = 12 mm. Density of ice = 913 $ kg/m^3 $. Find the vertical sag.

A 50 Hz, 3-$\phi$, 100 km long transmission line has a total resistance of 35 $ \Omega $, series reactance of 140 $ \Omega $ and shunt admittance (line to neutral) $ 930 \times 10^{-6} $ mho. It delivers 40 MW at 220 kV at 0.9 p.f. lagging. Using nominal $ \pi $ method determine the following: (a) A, B, C, D constants (b) Sending end voltage (c) Sending end current (d) Sending end power factor (e) Voltage regulation (f) Transmission efficiency.

Derive the expressions for voltage and current distributions over a longline. Explain the significance of characteristic impedance loading in connection with the longlines. Deduce the above voltage and current relations in the hyperbolic form and obtain the element values of an equivalent to represent the longlines.

Explain briefly the following methods of grading of cables: (a) Capacitance grading (b) Intersheath grading.

For a medium length transmission line, A is

To increase the transmission capability of a high-voltage longline

The surge impedance of 50-mile long underground cable is 50 ohms. For a length of 25 miles the impedance will be

In a transmission system, the weight of copper used is proportional to

Stringing chart is useful for

The regulation of a line at full-load 0.8 of lagging is 12%. The regulation at full-load 0.8 p.f. leading can be

The inductance of a line is minimum when

Which distribution system is more reliable?

In a 3-core cable, the capacitance between 2 conductors (with sheath earthed) is 3 $ \mu F $. The capacitance/phase is

For a transmission line with resistance R2, reactance X2 and negligible capacitance, the parameter A is

Describe the various systems of power transmission and compare the following as regard to the amount of copper used for the same distance, the same power transfer, the same maximum voltage to ground and the same power loss: (a) 3-phase, 3-wire AC (b) 3-wire DC (c) 1-phase, 2-wire AC.

State Kelvin's law and explain why in practice the law is usually not strictly observed.

The following data relate to a 2-wire feeder: Current carried throughout the year = 220 A. The portion of the capital cost which is proportional to X-sectional area = 6 per kg of Cu conductor. Cost of energy = 6 P per kWh. Interest and depreciation charges = 10% PA. Density of copper = 8.93 $ g/cm^3 $. Specific resistance of copper = 1.8 $ \mu\Omega-cm $. Find the most economical X-section of the conductor.

A 1.5 km long single-phase 2-wire feeder supplies the loads as under: 60 A at 0.8 p.f. (lagging), 600 m from the fed point. 40 A at 0.85 p.f. (lagging), 1200 m from the fed point. 50 A at 0.88 p.f. (lagging), 1500 m from the fed point. The resistance and reactance of the feeder per km length (go and return) are 0.1 $ \Omega $ and 0.2 $ \Omega $ respectively. If the voltage at the far end is to be maintained at 220 V, calculate the voltage of the sending end, and its phase angle with respect to the receiving end voltage.

Find the inductance per phase of 3-$\phi$ overhead transmission line using 2 cm diameter conductors when these are placed at the corners of equilateral triangle of sides 4 meters. Also do the derivation needful.

The three conductors of a 3-$\phi$ transmission line are arranged in a horizontal plane and are 4 meters apart. The diameter of each conductor is 2.5 cm. Determine the inductance per km of the each conductor (line to neutral). Assume balanced load and R, Y, B phase sequence. Determine the average inductance per phase for regularly transposed line.

Discuss the effect of wind and ice on sag.

The following data refers to a transmission line supported on level supports: Span length = 220 meters. Hard drawn copper conductor: X-sectional area = 120 $ mm^2 $, 37/2-11 mm; $ W_c = 1/2 $ kg/m. Ultimate tensile stress = 42.2 $ kg/mm^2 $. Factor of safety = 4. Wind pressure = 55 $ kg/m^2 $. Thickness of ice coating = 12 mm. Density of ice = 913 $ kg/m^3 $. Find the vertical sag.

A 50 Hz, 3-$\phi$, 100 km long transmission line has a total resistance of 35 $ \Omega $, series reactance of 140 $ \Omega $ and shunt admittance (line to neutral) $ 930 \times 10^{-6} $ mho. It delivers 40 MW at 220 kV at 0.9 p.f. lagging. Using nominal $ \pi $ method determine the following: (a) A, B, C, D constants (b) Sending end voltage (c) Sending end current (d) Sending end power factor (e) Voltage regulation (f) Transmission efficiency.

Derive the expressions for voltage and current distributions over a longline. Explain the significance of characteristic impedance loading in connection with the longlines. Deduce the above voltage and current relations in the hyperbolic form and obtain the element values of an equivalent to represent the longlines.

Explain briefly the following methods of grading of cables: (a) Capacitance grading (b) Intersheath grading.

The electric power can be transmitted by

In a transmission system, the weight of copper used is proportional to

ACSR conductors have

Stranded conductors usually have a central wire around which there are successive layers of 6, 12, 18, 24 wires. For n-layers, the total number of individual wires is

The inductance of two-wire power transmission line per km gets doubled when the

120 km long transmission line is considered as a

Percentage regulation of a transmission line is given by the expression

Sheaths are used in cables to

The charging current drawn by the cable

Transmission line constants are

Derive the Kelvin's law for most economical size of conductor.

The cost per km for each of the copper conductor of a section a sq. cm for a transmission line is $ Rs.(2800a + 1300) $. The load factor of the load current is 80% and the load factor for the losses is 65%. The rate of interest and depreciation is 10% and the cost of energy is 5 paisa per kW-h. Find the most economical current density for the transmission line by the use of Kelvin's law. Given $ \rho = 1.78 \times 10^{-8} \Omega-m $.

The following data refers to a 50 Hz, 1-$\phi$ transmission line: Length = 20 km. Load delivered at receiving end 5 MW at 118. Resistance of each conductor = 0.02 $ \Omega/km $. Inductance of conductor = 0.65 mH/km. The voltage at the receiving end is required to be kept at 10 kV. Find (a) sending end voltage and voltage regulation of the line; (b) the value of capacitors to be placed parallel with the load such that regulation is reduced to 50% of the obtained in (a). Compare the transmission efficiencies in parts (a) and (b).

Prove that the vol. gradient at surface of conductor in the cable will be minimum when $ \frac{R}{r} = e $ where r is the radius of conductor and R is the inner radius of sheath.

Enumerate the different types of losses in a cable. Also, derive the expression for dielectric loss.

A single-core lead covered cable is to be designed for 66 kV to earth. Its conductor radius is 0.5 cm and its three insulating materials A, B and C have relative permittivities 4, 2.5 and 4 with maximum permissible stresses of 50, 30 and 40 kV/cm respectively. Determine the minimum internal diameter of lead sheath. Discuss the arrangement of insulating materials.

Derive the expression for tension and sag in conductors if supports of equal height are used.

A transmission line conductor consists of hard drawn copper conductor 120 $ mm^2 $ cross-section, the conductor used is 37/2 mm having weight of 1118 kg/km and has a span of 200 meters. The supporting structures being level. The conductor has an ultimate tensile stress of 122 $ kg/mm^2 $ and allowable tension is not to exceed 1/4th of ultimate strength. Find (a) sag in still air, (b) sag with wind pressure of 60 $ kg/m^2 $, (c) sag with the wind pressure in part b and an ice coating of 10 mm. Also, find the vertical sag under this condition. Assume density of ice as 0.915 gm/cc.

Determine the inductance of the double circuit line shown in figure below. The self GMD of the conductor is 0.0069 meter.

Prove that the capacitance of a 3-$\phi$ unsymmetrically spaced transposed transmission line is given by $ c = \frac{2\pi\epsilon_0}{\ln \frac{\sqrt[3]{abc}}{r}} $ F/meter where a, b, c are the spacing between the conductors of different phases and r is radius of conductor.

The electric power can be transmitted by

In a transmission system, the weight of copper used is proportional to

ACSR conductors have

Stranded conductors usually have a central wire around which there are successive layers of 6, 12, 18, 24 wires. For n-layers, the total number of individual wires is

The inductance of two-wire power transmission line per km gets doubled when the

120 km long transmission line is considered as a

Percentage regulation of a transmission line is given by the expression

Sheaths are used in cables to

The charging current drawn by the cable

Transmission line constants are

Derive the Kelvin's law for most economical size of conductor.

The cost per km for each of the copper conductor of a section a sq. cm for a transmission line is $ Rs.(2800a + 1300) $. The load factor of the load current is 80% and the load factor for the losses is 65%. The rate of interest and depreciation is 10% and the cost of energy is 5 paisa per kW-h. Find the most economical current density for the transmission line by the use of Kelvin's law. Given $ \rho = 1.78 \times 10^{-8} \Omega-m $.

The following data refers to a 50 Hz, 1-$\phi$ transmission line: Length = 20 km. Load delivered at receiving end 5 MW at 118. Resistance of each conductor = 0.02 $ \Omega/km $. Inductance of conductor = 0.65 mH/km. The voltage at the receiving end is required to be kept at 10 kV. Find (a) sending end voltage and voltage regulation of the line; (b) the value of capacitors to be placed parallel with the load such that regulation is reduced to 50% of the obtained in (a). Compare the transmission efficiencies in parts (a) and (b).

Prove that the vol. gradient at surface of conductor in the cable will be minimum when $ \frac{R}{r} = e $ where r is the radius of conductor and R is the inner radius of sheath.

Enumerate the different types of losses in a cable. Also, derive the expression for dielectric loss.

A single-core lead covered cable is to be designed for 66 kV to earth. Its conductor radius is 0.5 cm and its three insulating materials A, B and C have relative permittivities 4, 2.5 and 4 with maximum permissible stresses of 50, 30 and 40 kV/cm respectively. Determine the minimum internal diameter of lead sheath. Discuss the arrangement of insulating materials.

Derive the expression for tension and sag in conductors if supports of equal height are used.

A transmission line conductor consists of hard drawn copper conductor 120 $ mm^2 $ cross-section, the conductor used is 37/2 mm having weight of 1118 kg/km and has a span of 200 meters. The supporting structures being level. The conductor has an ultimate tensile stress of 122 $ kg/mm^2 $ and allowable tension is not to exceed 1/4th of ultimate strength. Find (a) sag in still air, (b) sag with wind pressure of 60 $ kg/m^2 $, (c) sag with the wind pressure in part b and an ice coating of 10 mm. Also, find the vertical sag under this condition. Assume density of ice as 0.915 gm/cc.

Determine the inductance of the double circuit line shown in figure below. The self GMD of the conductor is 0.0069 meter.

Prove that the capacitance of a 3-$\phi$ unsymmetrically spaced transposed transmission line is given by $ c = \frac{2\pi\epsilon_0}{\ln \frac{\sqrt[3]{abc}}{r}} $ F/meter where a, b, c are the spacing between the conductors of different phases and r is radius of conductor.