Electrical Circuit Analysis

Kirchhoff's Current law is based on law of conservation of

Determine the current if a 20 coulomb charge passes a point in 0.25 seconds

Comment on the linearity of $ y[n]=n*x[n] $.

Maximum power transfer occurs at a

The inverse laplace transform of $ \frac{1}{s} - \frac{e^{-as}}{s} $ is

The parameter A of a two port network is equal to

A system is linear if it satisfies

Given $ F(S)=(S+2)/S(S+1) $ the initial and final values of f(t) will be respectively

Time constant of RL circuit is

The transmission parameters are also known as:

A series R-L circuit has $ R=2 \Omega $ and $ L=2H $. A ramp input r(t) is applied at $ t=1 \text{ sec} $. Obtain an expression for current through the circuit.

Define time constant. What the significance of time constant?

State Superposition theorem explaining the conditions in which it is valid.

In the network shown in figure below, find the value of current flowing through the 6 ohm resistance in the circuit given below using superposition theorem.

State and explain Thevenin's Theorem. Show the Thevenin's equivalent representation of any circuit.

For the circuit given below, determine the current flowing through the 4 ohm resistance by Thevenin's theorem. What are the values of Thevenin's resistance and Thevenin's voltage for this circuit.

Calculate the Laplace Transform of the function $ f(t)=e^{-t}\sin(wt) $.

Define Gate function? Using Gate function find out the Laplace Transform of a single Sine wave.

Calculate the impedance, resistance, Power and power factor of a circuit whose expression for voltage and current are given by: $ V = 100\sin(wt+60^{\circ}) - 50\sin(5wt-30^{\circ}) \text{ volt} $ and $ I = 10\sin(wt+60^{\circ}) - 5\sin(3wt+30^{\circ}) \text{ amp} $.

A 400 mH coil of zero resistance is connected to an AC circuit in which 6 mA current is flowing. Find out the voltage across the coil if the frequency is 100 Hz.

Obtain the Y & Z parameters of the network shown below. Write the unit of all individual parameters.

Explain frequency response. Why magnitude and phase plots are necessary for frequency response analysis.

What is Q-factor? Calculate the quality factor of a series RLC circuit with $ L=2H $, $ C=2\mu F $ and $ R=20 \Omega $.

Kirchhoff's Current law is based on law of conservation of

Determine the current if a 20 coulomb charge passes a point in 0.25 seconds

Comment on the linearity of $ y[n]=n*x[n] $.

Maximum power transfer occurs at a

The inverse laplace transform of $ \frac{1}{s} - \frac{e^{-as}}{s} $ is

The parameter A of a two port network is equal to

A system is linear if it satisfies

Given $ F(S)=(S+2)/S(S+1) $ the initial and final values of f(t) will be respectively

Time constant of RL circuit is

The transmission parameters are also known as:

A series R-L circuit has $ R=2 \Omega $ and $ L=2H $. A ramp input r(t) is applied at $ t=1 \text{ sec} $. Obtain an expression for current through the circuit.

Define time constant. What the significance of time constant?

State Superposition theorem explaining the conditions in which it is valid.

In the network shown in figure below, find the value of current flowing through the 6 ohm resistance in the circuit given below using superposition theorem.

State and explain Thevenin's Theorem. Show the Thevenin's equivalent representation of any circuit.

For the circuit given below, determine the current flowing through the 4 ohm resistance by Thevenin's theorem. What are the values of Thevenin's resistance and Thevenin's voltage for this circuit.

Calculate the Laplace Transform of the function $ f(t)=e^{-t}\sin(wt) $.

Define Gate function? Using Gate function find out the Laplace Transform of a single Sine wave.

Calculate the impedance, resistance, Power and power factor of a circuit whose expression for voltage and current are given by: $ V = 100\sin(wt+60^{\circ}) - 50\sin(5wt-30^{\circ}) \text{ volt} $ and $ I = 10\sin(wt+60^{\circ}) - 5\sin(3wt+30^{\circ}) \text{ amp} $.

A 400 mH coil of zero resistance is connected to an AC circuit in which 6 mA current is flowing. Find out the voltage across the coil if the frequency is 100 Hz.

Obtain the Y & Z parameters of the network shown below. Write the unit of all individual parameters.

Explain frequency response. Why magnitude and phase plots are necessary for frequency response analysis.

What is Q-factor? Calculate the quality factor of a series RLC circuit with $ L=2H $, $ C=2\mu F $ and $ R=20 \Omega $.

A 10 mH inductor carries a sinusoidal current of 1 A r.m.s at a frequency of 50 Hz. The average power dissipated by the inductor is

Thevenin's equivalent circuit consists of

When the two quantities are in quadrature, the phase angle between them will be.

A two-port network is symmetrical if

A two element series circuit is connected across an AC source given by $ e=200\sqrt{2}\sin(314t+20)V $, the current is found to be $ i=10\sqrt{2}\cos(314t-25)A $. The parameters of the circuit are

Superposition theorem is not applicable to networks containing

Which of the following is the Passive elements?

When a unit impulse voltage is applied to an inductor of 1 H, the energy supplied by the source is

There are no transients in pure resistance circuits because they

When a number of two-port network is cascaded, then

Two mutually coupled identical coils are connected in series having self-inductance $ L=4 \text{ mH} $ and mutual inductance $ M=2 \text{ mH} $.
What are the maximum and minimum possible values of equivalent inductances?

Determine the coefficient of coupling between the coils.

Prove that the average power in an AC circuit is given by $ W=VI\cos\phi $, where symbols have their usual meanings.

A voltage of $ e(t)=150\sin(1000t) $ is applied across a series R-L-C circuit, where $ R=40\Omega $, $ L=0.13 \text{ H} $ and $ C=10\mu F $. (i) Compute the r.m.s value of the steady-state current. (ii) Find the r.m.s voltage across the inductor. (iii) Find the r.m.s voltage across the capacitor. (iv) Determine the active and reactive power supplied by the source.

Find the Laplace transform of $ f(t)=e^{-at}\cos(\omega t) $, $ a>0 $.

Calculate the inverse Laplace transform of $ F(s)=\frac{1}{s(s^{2}-a^{2})} $.

In the series R-C circuit, the capacitor has an initial charge 2.5 mC. At $ t=0 $, the switch is closed and a constant voltage source $ V=100 \text{ V} $ is applied. Use the Laplace transform method to find the current in the circuit after closing the switch.

Two impedances $ Z_{1}=40\angle 30^{\circ} $ and $ Z_{2}=30\angle 60^{\circ} \Omega $ are connected in series across a single-phase 230 V, 50 Hz supply. Calculate the (i) Current drawn (ii) pf, and (iii) power consumed by the circuit.

State and explain the Super Position Theorem and find out the step to be followed in super position theorem.

State maximum power transfer theorem. Prove that efficiency of the circuit under maximum power transfer condition is 50%.

Draw the Thevenin equivalent circuit of the figure shown below and hence find the current through $ R=2\Omega $.

Find the current in a series RL circuit having $ R=2\Omega $ and $ L=10H $ while a d.c voltage of 100v is applied. What is the value of this current after 5 secs of switching on?

A steady state condition is reached with 100v d.c source. At $ t=0 $, switch K is suddenly open. Find the expression of current through the inductor after $ t=0.5 \text{ sec} $.

Define apparent power and Reactive power.

The current in a circuit lag the voltage by $ 30^{\circ} $ if the power be 400 w and the supply voltage be $ v=100\sin(377t+10^{\circ}) $ find complex power.

In an ac circuit $ v=100\sin(wt+30^{\circ})V $, $ I=5\sin(wt-30^{\circ})A $. find apparent power, real power and reactive power.

A 10 mH inductor carries a sinusoidal current of 1 A r.m.s at a frequency of 50 Hz. The average power dissipated by the inductor is

Thevenin's equivalent circuit consists of

When the two quantities are in quadrature, the phase angle between them will be.

A two-port network is symmetrical if

A two element series circuit is connected across an AC source given by $ e=200\sqrt{2}\sin(314t+20)V $, the current is found to be $ i=10\sqrt{2}\cos(314t-25)A $. The parameters of the circuit are

Superposition theorem is not applicable to networks containing

Which of the following is the Passive elements?

When a unit impulse voltage is applied to an inductor of 1 H, the energy supplied by the source is

There are no transients in pure resistance circuits because they

When a number of two-port network is cascaded, then

Two mutually coupled identical coils are connected in series having self-inductance $ L=4 \text{ mH} $ and mutual inductance $ M=2 \text{ mH} $.
What are the maximum and minimum possible values of equivalent inductances?

Determine the coefficient of coupling between the coils.

Prove that the average power in an AC circuit is given by $ W=VI\cos\phi $, where symbols have their usual meanings.

A voltage of $ e(t)=150\sin(1000t) $ is applied across a series R-L-C circuit, where $ R=40\Omega $, $ L=0.13 \text{ H} $ and $ C=10\mu F $. (i) Compute the r.m.s value of the steady-state current. (ii) Find the r.m.s voltage across the inductor. (iii) Find the r.m.s voltage across the capacitor. (iv) Determine the active and reactive power supplied by the source.

Find the Laplace transform of $ f(t)=e^{-at}\cos(\omega t) $, $ a>0 $.

Calculate the inverse Laplace transform of $ F(s)=\frac{1}{s(s^{2}-a^{2})} $.

In the series R-C circuit, the capacitor has an initial charge 2.5 mC. At $ t=0 $, the switch is closed and a constant voltage source $ V=100 \text{ V} $ is applied. Use the Laplace transform method to find the current in the circuit after closing the switch.

Two impedances $ Z_{1}=40\angle 30^{\circ} $ and $ Z_{2}=30\angle 60^{\circ} \Omega $ are connected in series across a single-phase 230 V, 50 Hz supply. Calculate the (i) Current drawn (ii) pf, and (iii) power consumed by the circuit.

State and explain the Super Position Theorem and find out the step to be followed in super position theorem.

State maximum power transfer theorem. Prove that efficiency of the circuit under maximum power transfer condition is 50%.

Draw the Thevenin equivalent circuit of the figure shown below and hence find the current through $ R=2\Omega $.

Find the current in a series RL circuit having $ R=2\Omega $ and $ L=10H $ while a d.c voltage of 100v is applied. What is the value of this current after 5 secs of switching on?

A steady state condition is reached with 100v d.c source. At $ t=0 $, switch K is suddenly open. Find the expression of current through the inductor after $ t=0.5 \text{ sec} $.

Define apparent power and Reactive power.

The current in a circuit lag the voltage by $ 30^{\circ} $ if the power be 400 w and the supply voltage be $ v=100\sin(377t+10^{\circ}) $ find complex power.

In an ac circuit $ v=100\sin(wt+30^{\circ})V $, $ I=5\sin(wt-30^{\circ})A $. find apparent power, real power and reactive power.

The voltage across a 1.1-kW toaster that produces a current of 10 A is

The current $I$ in the following circuit is

The current through a branch in a linear network is 2 A when the input source voltage is 10 V. If the voltage is reduced to 1 V and the polarity is reversed, the current through the branch is

A load is connected to a network. At the terminals to which the load is connected, $R_{th} = 10\ \Omega$ and $V_{th} = 20\text{ V}$. The maximum possible power supplied to the load is

If a two-port is reciprocal, which of the following is not true?

For the three coupled coils in the following figure, calculate the total inductance:

A network which contains one or more source of e.m.f. is known as

The circuit having some properties for either direction of current is known as ___ circuit.

Which of the following theorems can be applied to linear, non-linear, active, passive, time-variant, time-invariant, all kinds of circuits?

Ideal current source has

Using nodal analysis, find $I_o$ and $V_o$ in the following circuit :

Apply mesh analysis to find $i$ in the following figure :

(i) In the following circuit, calculate $V_o$ and $I_o$ when $V_s = 1\text{ V}$. (ii) Find $V_o$ and $I_o$ when $V_s = 10\text{ V}$. (iii) What are $V_o$ and $I_o$ when each of the $1\ \Omega$ resistors is replaced by a $10\ \Omega$ resistor and $V = 10\text{ V}$?

What do you understand by resonance? For a series $R-L-C$ circuit, derive the formula for (i) resonance frequency and (ii) cut-off frequency.

Explain the pole zero concept. How does this concept provide the knowledge of a stable system?

Use the superposition principle to find $V_o$ and $I_o$ in the circuit below:

Determine $R_{th}$ and $V_{th}$ at terminals 1-2 of each of the circuits drawn below :

State and describe maximum power transfer theorem with a suitable example.

Compute the value of $R$ for which maximum power transfer can be offered to $10\ \Omega$ resistor in the following figure. Also find the maximum power that can be transferred.

Find $v_o(t)$, using Laplace transform. Consider initial conditions to be zero. (i) If the switch in the circuit below, has been opened for a long time and is closed at $t = 0$. (ii) Suppose that the switch has been closed for a long time and is opened at $t = 0$.

Determine the step response $V_o(t)$ to $V_s = 9u(t)\text{ V}$ in the following circuit without using Laplace transform.

For the bridge circuit in the following figure, obtain— (i) the $z$-parameters; (ii) the $h$-parameters; (iii) the transmission parameters using the parameters obtained in parts (i) and (ii) separately. Compare the results obtained.

The Norton's equivalent of the circuit shown in figure below is

A 10 mH inductor carries a sinusoidal current of 1 A r.m.s. at a frequency of 50 Hz. The average power dissipated by the inductor is

Thevenin's equivalent circuit consists of

A two-element series circuit is connected across an AC source given by $ e=200\sqrt{2}\sin(314t+20) \text{ V} $. The current is found to be $ i=10\sqrt{2}\cos(314t-25) \text{ A} $. Then parameters of the circuit are

There are no transients in pure resistance circuits because they

In the below network, the switch K is opened at $ t=0 $. Then $ \frac{dV}{dt} $ at $ t=0^{+} $ is

When a number of two-port network is cascaded, then

Two coils are coupled in such a way that the mutual inductance between them is 16 mH. If the inductances of the coils are 20 mH and 80 mH respectively, the coefficient of coupling is

When a unit impulse voltage is applied to an inductor of 1 H, the energy supplied by the source is

The h-parameters $ h_{11} $ and $ h_{22} $ are related to Z and Y-parameters as

Two mutually coupled identical coils are connected in series having self-inductance $ L=4 \text{ mH} $ and mutual inductance $ M=2 \text{ mH} $.
What are the maximum and minimum possible values of equivalent inductances?

Determine the coefficient of coupling between the coils.

Show that Thevenin's and Norton's theorems are dual to each other.

Using Norton's theorem, find the current in $ 5\Omega $ resistor for the circuit shown below.

When can a two-port circuit be declared as a reciprocal circuit?

Find ABCD parameters for the two-port network shown in the figure below:

Prove that the average power in an AC circuit is given by $ W=VI\cos\phi $, where symbols have their usual meanings.

A voltage of $ e(t)=150\sin(1000t) $ is applied across a series R-L-C circuit, where $ R=40\Omega $, $ L=0.13 \text{ H} $ and $ C=10\mu\text{F} $. (i) Compute the r.m.s. value of the steady-state current. (ii) Find the r.m.s. voltage across the inductor. (iii) Find the r.m.s. voltage across the capacitor. (iv) Determine the active and reactive power supplied by the source.

Determine overall Z-parameters when two 2-port networks with identical $ Z_{11}=Z_{12}=Z_{21}=Z_{22}=2\Omega $ are connected in cascade.

In the R-L-C circuit shown in figure below, $ I_{s}=10 \text{ A} $, $ R=1\Omega $, $ L=1\text{H} $, $ C=1\mu\text{F} $ and $ i_{L}(0^{-})=0 $. Determine the following parameters after the switch is closed at $ t=0 $: (a) $ V(0^{+}) $ (b) $ \frac{dV}{dt} $ at $ t=0^{+} $ (c) $ \frac{d^{2}V}{dt^{2}} $ at $ t=0^{+} $.

An R-L-C tank circuit is composed of components having values as $ R=0.2\Omega $, $ L=100 \text{ mH} $ and $ C=50\mu\text{F} $. Determine the resonance frequency and the corresponding input current at 24 V.

Obtain the values of R, L and C in a series R-L-C circuit that resonates at 1.5 kHz and consumes 50 W from a 50 V a.c. source operating at the resonance frequency. The bandwidth is 0.75 kHz.

For the circuit shown below, obtain the current through the capacitor C at $ t=0^{+} $ using Laplace transform following the switching takes place at $ t=0 $. Assume the capacitor to be initially discharged.

The Norton's equivalent of the circuit shown in figure below is

A 10 mH inductor carries a sinusoidal current of 1 A r.m.s. at a frequency of 50 Hz. The average power dissipated by the inductor is

Thevenin's equivalent circuit consists of

A two-element series circuit is connected across an AC source given by $ e=200\sqrt{2}\sin(314t+20) \text{ V} $. The current is found to be $ i=10\sqrt{2}\cos(314t-25) \text{ A} $. Then parameters of the circuit are

There are no transients in pure resistance circuits because they

In the below network, the switch K is opened at $ t=0 $. Then $ \frac{dV}{dt} $ at $ t=0^{+} $ is

When a number of two-port network is cascaded, then

Two coils are coupled in such a way that the mutual inductance between them is 16 mH. If the inductances of the coils are 20 mH and 80 mH respectively, the coefficient of coupling is

When a unit impulse voltage is applied to an inductor of 1 H, the energy supplied by the source is

The h-parameters $ h_{11} $ and $ h_{22} $ are related to Z and Y-parameters as

Two mutually coupled identical coils are connected in series having self-inductance $ L=4 \text{ mH} $ and mutual inductance $ M=2 \text{ mH} $.
What are the maximum and minimum possible values of equivalent inductances?

Determine the coefficient of coupling between the coils.

Show that Thevenin's and Norton's theorems are dual to each other.

Using Norton's theorem, find the current in $ 5\Omega $ resistor for the circuit shown below.

When can a two-port circuit be declared as a reciprocal circuit?

Find ABCD parameters for the two-port network shown in the figure below:

Prove that the average power in an AC circuit is given by $ W=VI\cos\phi $, where symbols have their usual meanings.

A voltage of $ e(t)=150\sin(1000t) $ is applied across a series R-L-C circuit, where $ R=40\Omega $, $ L=0.13 \text{ H} $ and $ C=10\mu\text{F} $. (i) Compute the r.m.s. value of the steady-state current. (ii) Find the r.m.s. voltage across the inductor. (iii) Find the r.m.s. voltage across the capacitor. (iv) Determine the active and reactive power supplied by the source.

Determine overall Z-parameters when two 2-port networks with identical $ Z_{11}=Z_{12}=Z_{21}=Z_{22}=2\Omega $ are connected in cascade.

In the R-L-C circuit shown in figure below, $ I_{s}=10 \text{ A} $, $ R=1\Omega $, $ L=1\text{H} $, $ C=1\mu\text{F} $ and $ i_{L}(0^{-})=0 $. Determine the following parameters after the switch is closed at $ t=0 $: (a) $ V(0^{+}) $ (b) $ \frac{dV}{dt} $ at $ t=0^{+} $ (c) $ \frac{d^{2}V}{dt^{2}} $ at $ t=0^{+} $.

An R-L-C tank circuit is composed of components having values as $ R=0.2\Omega $, $ L=100 \text{ mH} $ and $ C=50\mu\text{F} $. Determine the resonance frequency and the corresponding input current at 24 V.

Obtain the values of R, L and C in a series R-L-C circuit that resonates at 1.5 kHz and consumes 50 W from a 50 V a.c. source operating at the resonance frequency. The bandwidth is 0.75 kHz.

For the circuit shown below, obtain the current through the capacitor C at $ t=0^{+} $ using Laplace transform following the switching takes place at $ t=0 $. Assume the capacitor to be initially discharged.

Find the current I in the circuit of Fig. 1 by using the superposition theorem. [DIAGRAM INSTRUCTION: A circuit with a 1A upward current source, a parallel 4 ohm resistor, followed by a T-network (1 ohm, 2 ohm, 3 ohm) and a 1V DC source.]

In Fig. 2, find the value of $ R_{Th} $ and $ I_{SC} $.

Find the value of $ R_{L} $ of Fig. 3 so that the maximum power can be transferred. [DIAGRAM INSTRUCTION: A circuit with two DC sources and an independent 1A current source, mixed with 10 ohm resistors, ending in load resistor RL.]

Find the Z-parameters of the two-port network shown in Fig. 4.

Two coupled coils have self-inductances $ L_{1}=50 \text{ mH} $ and $ L_{2}=200 \text{ mH} $ and a coefficient of coupling $ k=0.5 $. If coil 2 has 1000 turns, and $ i_{1}=5.0\sin(400t)\text{A} $, find the voltage at coil 2.

four 2-mark questions are missing

Use the superposition theorem in the circuit shown in Fig. 7 to find current I. [DIAGRAM INSTRUCTION: A 10V DC source connected to a 5 ohm resistor, a dependent voltage source $ 2V_{x} $, a shunt 2 ohm resistor (with voltage $ V_{x} $), and a 2A independent current source.]

Draw the Thévenin's equivalent circuit of Fig. 8 and hence find the current through $ R=2\Omega $. (All the resistances shown in the figure are in ohm).

State compensation theorem.

Find the current $ I_{0} $ of Fig. 9 using the superposition theorem.

In the circuit of Fig. 10, find the effective value of the resistance seen by the source $ V_{s} $.

Define incidence matrix. Find the complete incidence matrix of the graph shown in Fig. 11.

Define the g-parameters of an electrical circuit.

Find the g-parameters in the circuit shown in Fig. 12.

Find the Z-parameters and Y-parameters of the circuit shown in Fig. 13.

Find the Laplace transform of $ f(t)=e^{-\alpha t}\cos(\omega t) $, $ \alpha>0 $.

Calculate the inverse Laplace transform of $ F(s)=\frac{1}{s(s^{2}-a^{2})} $.

In the series R-C circuit, the capacitor has an initial charge 2.5 mC. At $ t=0 $, the switch is closed and a constant-voltage source $ V=100\text{ V} $ is applied. Use the Laplace transform method to find the current in the circuit after closing the switch.

Draw the graph for the given incidence matrix:
$ [A] = \begin{bmatrix} -1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & -1 & 0 & 0 & 0 & -1 & 1 \\ 0 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 \end{bmatrix} $

Find the cut-set matrix from the graph as shown in Fig. 14.

Consider the network shown in Fig. 15, draw the graph and determine (i) number of links, (ii) rank of the graph and (iii) total number of trees.

State the characteristics of an ideal transformer.

Define r.m.s. value, form factor, peak factor, complex power and half power frequency.

Calculate the resonant frequency of a series R-L-C circuit.

Obtain the current in each branch of the network shown in Fig. 16, using the mesh current method.

Obtain the total power supplied by the 60 V source and the power absorbed in each resistor in the network of Fig. 17.

Compute the mesh currents of Fig. 18.

Define supermesh and supernode.

Derive step response of a series R-C circuit.

Define forced response and natural response.

For the circuit shown in Fig. 19, the switch K is moved from position 1 to position 2 at $ t=0 \text{ s} $. Find the current $ i(t) $ assuming $ i(0_{-})=2\text{ A} $ and $ V_{c}(0_{+})=2\text{ V} $.

Find the current I in the circuit of Fig. 1 by using the superposition theorem. [DIAGRAM INSTRUCTION: A circuit with a 1A upward current source, a parallel 4 ohm resistor, followed by a T-network (1 ohm, 2 ohm, 3 ohm) and a 1V DC source.]

In Fig. 2, find the value of $ R_{Th} $ and $ I_{SC} $.

Find the value of $ R_{L} $ of Fig. 3 so that the maximum power can be transferred. [DIAGRAM INSTRUCTION: A circuit with two DC sources and an independent 1A current source, mixed with 10 ohm resistors, ending in load resistor RL.]

Find the Z-parameters of the two-port network shown in Fig. 4.

Two coupled coils have self-inductances $ L_{1}=50 \text{ mH} $ and $ L_{2}=200 \text{ mH} $ and a coefficient of coupling $ k=0.5 $. If coil 2 has 1000 turns, and $ i_{1}=5.0\sin(400t)\text{A} $, find the voltage at coil 2.

four 2-mark questions are missing

Use the superposition theorem in the circuit shown in Fig. 7 to find current I. [DIAGRAM INSTRUCTION: A 10V DC source connected to a 5 ohm resistor, a dependent voltage source $ 2V_{x} $, a shunt 2 ohm resistor (with voltage $ V_{x} $), and a 2A independent current source.]

Draw the Thévenin's equivalent circuit of Fig. 8 and hence find the current through $ R=2\Omega $. (All the resistances shown in the figure are in ohm).

State compensation theorem.

Find the current $ I_{0} $ of Fig. 9 using the superposition theorem.

In the circuit of Fig. 10, find the effective value of the resistance seen by the source $ V_{s} $.

Define incidence matrix. Find the complete incidence matrix of the graph shown in Fig. 11.

Define the g-parameters of an electrical circuit.

Find the g-parameters in the circuit shown in Fig. 12.

Find the Z-parameters and Y-parameters of the circuit shown in Fig. 13.

Find the Laplace transform of $ f(t)=e^{-\alpha t}\cos(\omega t) $, $ \alpha>0 $.

Calculate the inverse Laplace transform of $ F(s)=\frac{1}{s(s^{2}-a^{2})} $.

In the series R-C circuit, the capacitor has an initial charge 2.5 mC. At $ t=0 $, the switch is closed and a constant-voltage source $ V=100\text{ V} $ is applied. Use the Laplace transform method to find the current in the circuit after closing the switch.

Draw the graph for the given incidence matrix:
$ [A] = \begin{bmatrix} -1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & -1 & 0 & 0 & 0 & -1 & 1 \\ 0 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 \end{bmatrix} $

Find the cut-set matrix from the graph as shown in Fig. 14.

Consider the network shown in Fig. 15, draw the graph and determine (i) number of links, (ii) rank of the graph and (iii) total number of trees.

State the characteristics of an ideal transformer.

Define r.m.s. value, form factor, peak factor, complex power and half power frequency.

Calculate the resonant frequency of a series R-L-C circuit.

Obtain the current in each branch of the network shown in Fig. 16, using the mesh current method.

Obtain the total power supplied by the 60 V source and the power absorbed in each resistor in the network of Fig. 17.

Compute the mesh currents of Fig. 18.

Define supermesh and supernode.

Derive step response of a series R-C circuit.

Define forced response and natural response.

For the circuit shown in Fig. 19, the switch K is moved from position 1 to position 2 at $ t=0 \text{ s} $. Find the current $ i(t) $ assuming $ i(0_{-})=2\text{ A} $ and $ V_{c}(0_{+})=2\text{ V} $.