Questions & Answers of Electric Circuits

The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

•  (A) 11
•  (B) 12
•  (C) 13
•  (D) 14

In the figure, the voltages are $ v_1(t)=100\cos\left(wt\right),\;v_2(t)=100\cos\left(wt+\mathrm\pi18\right)\;\; $ and $ v_3(t)=100\cos\left(wt+\mathrm\pi36\right) $. The circuit is in sinusoidal steady state, and $ R<<wL.P_1,P_2\; $ and $ P_3 $ are the average power outputs. Which one of the following statements is true?

•  (A) $ \style{font-family:'Times New Roman'}{P_1=P_2=\;P_3=0} $
•  (B) $ \style{font-family:'Times New Roman'}{P_1<0,=P_2>0,\;P_3>0} $
•  (C) $ \style{font-family:'Times New Roman'}{P_1<0,=P_2>0,\;P_3<0} $
•  (D) $ \style{font-family:'Times New Roman'}{P_1>0,=P_2<0,\;P_3>0} $

In the two-port network shown, the $ \style{font-family:'Times New Roman'}{h_{11}} $ parameter $ \style{font-family:'Times New Roman'}{\left(where\;h_{11}=\frac{V_1}{I_1}\;when\;V_2=0\right)} $ in ohms is _____________ (up to 2 decimal places).

A DC voltage source is connected to a series L-C circuit by turning on the switch S at time $ t=0 $ as shown in the figure. Assume $ i(0)=0,v(0)=0 $ . Which one of the following circular loci represents the plot of $ i(t) $ versus $ v(t)\;? $

•  (A) 
•  (B) 
•  (C) 
•  (D) 

The equivalent impedance $ Z_{eq} $ for the infinite ladder circuit shown in the figure is

•  (A) $ j12\;\Omega $
•  (B) $ -j12\;\Omega $
•  (C) $ j13\;\Omega $
•  (D) $ 13\;\Omega $

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $ V_{an}=100\angle0^\circ\; $ V ,$ V_{bn}=100\angle-120^\circ\; $ V and $ V_{cn}=100\angle-240^\circ\; $ V  (angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________$ \Omega $ (up to 2 decimal places).

The voltage across the circuit in the figure, and the current through it, are given by the following expressions

$ v(t)=5-10\;\cos\left(wt+60^\circ\right) V $

$ i(t)=5+X\;\cos\left(wt\right)A $

where $ w=100\mathrm\pi $ radian/s. If the average power delivered to the circuit is zero, then the value of $ \mathrm X $ (in Ampere) is _____ (up to 2 decimal places).

The voltage $ v(t) $ across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency $ w=100 $radian/s. When the inductor current $ i(t) $ is in phase with the voltage $ v(t) $, the magnitude of the impedance Z (in $ \mathrm\Omega $) seen between the terminals a and b is ________ (up to 2 decimal places).

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $ V_{an}=220\;\sin\left(100\;\mathrm{πt}\right)\;V $ and $ i_a=10\;\sin\left(100\;\mathrm{πt}\right)\;A, $ respectively. Similarly for phase-b, the instantaneous voltage and current are $ V_{bn}=220\;\cos\left(100\;\mathrm{πt}\right)\;V $ and $ i_b=10\;\cos\left(100\;\mathrm{πt}\right)\;A, $, respectively.

The total instantaneous power flowing from the source to the load is

•  (A) $ 2200\;W $
•  (B) $ 2200\;\sin^2\;(100\mathrm\pi t)\;W $
•  (C) $ 4400\;W $
•  (D) $ 2200\;\sin\;(100\mathrm{πt})\;\cos\;(100\mathrm{πt})W $

The power supplied by the 25 V source in the figure shown below is _________ W.

The equivalent resistance between the terminal A and B is__________$ \Omega$.

Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

Given

                       $ \begin{array}{l}V_1=A_1V_2+B_1I_2\\I_1=C_1V_2+D_1I_2\\V_2=A_2V_3+B_2I_3\\I_2=C_2V_3+D_2I_3\end{array} $

$ A1,\;B1,\;C1,\;D1,\;A2,\;B2,\;C2 $ and $ D_2 $ are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source $ V_T $ and an impendence $ Z_T $ , connected in series, then

•  (A) $V_T=\frac{V_1}{A_1A_2},Z_T\frac{A_1B_2+B_1D_2}{A_1A_2+B_1C_2}$
•  (B) $ V_T=\frac{V_1}{A_1A_2+B_1C_2},\;Z_T\frac{A_1B_2+B_1D_2}{A_1A_2} $
•  (C) $ V_T=\frac{V_1}{A_1A_2},\;Z_T\frac{A_1B_2+B_1D_2}{A_1A_2} $
•  (D) $ V_T=\frac{V_1}{A_1A_2+B_1C_2},Z_T\frac{A_1B_2+B_1D_2}{A_1A_2+B_1C_2} $

The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for $t \ge 0$, is

•  (A) 2.5e ^-4t
•  (B) 5e ^-4t
•  (C) 2.5e ^-0.25t
•  (D) 5e ^-0.25t

In the circuit shown below, the maximum power transferred to the resistor R is ______________ W.

The figure shows the power per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where $\alpha$ is a complex number with non-zero real and imaginary parts.

For the given circuit, Y_bus and Z_bus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 × 2. Which one of the following statements is true?

•  (A) Both Y_bus and Z_bus are symmetric
•  (B) Y_bus is symmetric and Z_bus is unsymmetric
•  (C) Y_bus is unsymmetric and Z_bus is symmetric
•  (D) Both Y_bus and Z_bus are unsymmetric

For the given 2-port network, the value of transfer impedance z₂₁ in ohms is__________

The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals_________.(Give the answer up to one decimal place.)

For the balanced Y-Y connected 3-phase in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

•  (A) $33\angle-53.1^\circ\Omega$
•  (B) $60\angle53.1^\circ\Omega$
•  (C) $60\angle-53.1^\circ\Omega$
•  (D) $180\angle-53.1^\circ\Omega$

In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

•  (A) 1 nF
•  (B) 1 µF
•  (C) 1 mF
•  (D) 10 mF

For the network given in figure below, the Thevenin’s voltage V_ab is

•  (A) -1.5 V
•  (B) -0.5 V
•  (C) 0.5 V
•  (D) 1.5 V

•  (A)  R_A=R_B
•  (B)  R_A=R_B=0
•  (C)  R_A< R_B
•  (D)  R_B= R_A /(1+R_A)

In the given circuit, the current supplied by the battery, in ampere, is _______.

•  (A)  $ nL $
•  (B)  $n^{2}L$
•  (C)  $\frac{n}{L}$
•  (D)  $\frac{n^2}{L}$

In the circuit shown below, the node voltage V_A is ___________ V.

•  (A)  65, 35 
•  (B)  50, 50
•  (C)  60, 90
•  (D)  60, 80

$v\left(t\right)=100\sin \left(\omega t\right)$ ,

$i\left(t\right)=10\sin \left(\omega t-{60}^{°}\right)+2\sin \left(3\omega t\right)+5\sin \left(5\omega t\right)$

The average power consumed by the load, in W, is___________.

•  (A)  0
•  (B)  5
•  (C)  10
•  (D)  20

•  (A)  2 and 5
•  (B)  5 and 2
•  (C)  3 and 4
•  (D)  4 and 3

The voltages developed across the 3 Ω and 2 Ω resistors shown in the figure are 6V and 2V respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5V voltage source?

•  (A) 5
•  (B) 7
•  (C) 10
•  (D) 14

For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage,$V_{Th}$(in volt), seen from terminal AB is _________.

An inductor is connected in parallel with a capacitor as shown in the figure.

As the frequency of current i is increased, the impedance (Z) of the network varies as

•  (A) 
•  (B) 
•  (C) 
•  (D) 

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt) is given by v(t) = 12 sin t. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______.

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5 V is applied to Port 1, a current of 1.25 A flows through a 1 $\mathrm{\Omega }$ resistance connected across Port 2. When 3 V is applied to Port 1, then current (in Ampere) through a 2 $\mathrm{\Omega }$ resistance connected across Port 2 is _________.

In the given circuit, the parameter k is positive, and the power dissipated in the 2 $\mathrm{\Omega }$ resistor is 12.5W. The value of k is________.

A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $\frac{{\mathrm{d}}^{2}i}{\mathrm{d}{t}^2}$ at t = $0^{+}$ is

•  (A)  $\frac{V}{L}$
•  (B)  $\frac{-V}{R}$
•  (C)  0
•  (D)  $\frac{-RV}{L^2}$

The current i (in Ampere) in the 2 $\mathrm{\Omega }$ resistor of the given network is ____ .

In the given network $V_1=100\angle 0^{° }$V, $V_2=100\angle -{120}^{°}$V, $V_3=100\angle +{120}^{°}$V. The phasor current i (in Ampere) is

•  (A)  173.2$\angle -{60}^{°}$
•  (B)  173.2$\angle {120}^{°}$
•  (C)  100.0$\angle -{60}^{°}$
•  (D)  100.0$\angle {120}^{°}$

A symmetrical square wave of 50% duty cycle has amplitude of ±15 V and time period of 0.4π ms. This square wave is applied across a series RLC circuit with R = 5$\mathrm{\Omega }$, L = 10 mH, and C = 4μF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is __________.

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $\alpha$L is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________.

C₀ is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity ${\mathit{\in }}_r$, the expression for the modified capacitance is

•  (A) $\frac{C_0}{2}\left(1+{\in }_r\right)$
•  (B) $\left(C_0+{\in }_r\right)$
•  (C) $\frac{C_0}{2}{\in }_r$
•  (D) $C_0\left(1+{\in }_r\right)$

A combination of 1 µF capacitor with an initial voltage${\nu }_c\left(0\right)=-2\nu$ in series with a 100 O resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0 s as shown. Which of the following graphs shown in the options approximates the voltage v_s across the current source over the next few seconds?

•  (A) 
•  (B) 
•  (C) 
•  (D) 

An incandescent lamp is marked 40 W, 240V. If resistance at room temperature (26°C) is 120 Ω, and temperature coefficient of resistance is 4.5x10^-3/°C, then its ‘ON’ state filament temperature in °C is approximately _______

In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ______

The following four vector fields are given in Cartesian co-ordinate system. The vector field which does not satisfy the property of magnetic flux density is

•  (A) $y^2{\mathbf{a}}_x+z^2{\mathbf{a}}_y+x^2{\mathbf{a}}_z$
•  (B) $z^2{\mathbf{a}}_x+x^2{\mathbf{a}}_y+x^2{\mathbf{a}}_z$
•  (C) $x^2{\mathbf{a}}_x+y^2{\mathbf{a}}_y+z^2{\mathbf{a}}_z$
•  (D) $y^2{z}^2{\mathbf{a}}_x+x^2{z}^2{\mathbf{a}}_y+z^2{y}^2{\mathbf{a}}_z$