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Consider a circuit shown below,

At steady state, the current through resistor is given by $15cost$ and the voltage across the inductor is $2\sin t$ .

The RMS value of the current through the capacitor is

A two-port network is represented by ABCD parameters given by



$\left[\begin{array}{c}{V}_1\\ I_1\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}{V}_2\\ -I_2\end{array}\right]$



If port-2 is terminated by $R_L$, the input impendance seen at port-1 is given by

1. 3.32

The equivalent capacitance of the input loop of the circuit shown is

In figure, the value of R is

Find the voltage $V_X$ in the figure shown

The parameter $h_{21}$ in terms of ABCD parameter is

The impedance seen by the source in the circuit in figure is given by

For the lattice circuit shown in the figure, $Z_B=j2\Omega$ and $Z_b=2\Omega$. The value of the open circuit impendance parameters $Z=\left[\begin{array}{cc}{Z}_{11}& Z_{12}\\ Z_{21}& Z_{22}\end{array}\right]$ are

If the current through a 0.1 H inductor is $i\left(t\right)=10t{e}^{-5t}A,$ then the energy stored at t=1 sec is

In the circuit shown below:



$(v_1+v_2)=\left[1sin\right(2\pi 10000t)+1sin(2\pi 30000t\left)\right]V$



The RMS value of the current through the resistor R will be minimum if the value of the capacitor C in microfarad is

1. 0.28

Given two coupled inductors $L_1$ and $L_2$, their mutual inductance $M$ satisfies

A capacitor of capacitance $C$ is charged to voltage $V_0$ and allowed to discharge through a resistance R while charge another capacitance${}^{\prime }\alpha C^{\prime }$. What fraction of total energy is lost at steady state?

A generator of internal impendance, $Z_G$, delivers maximum power to a load impendance, $Z_L$, only if $Z_L$ = __.

1. 0

The graph of an electrical network has $N$ nodes and $B$ branches. The number of links $L$, with respect to the choice of a tree, is given by

1. 115.5

Consider the circult shown in figure. Assume that at $t=0,-1$ A flows through the inductor and $+5V$ is across the capacitor. If $V_s=10u\left(t\right)V,$ then the value of the voltage across the capacitor is

The switch was in position (1) for long time and was moved to position (2) at $t=0$ is

$\frac{d^{2}i}{d{t}^2}$ at $t=0^{+}$

Twelve $1\Omega$ resistances are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is

The RC circuit shown below has a variable resistance R(t) given by the following expression:

$R\left(t\right)=R_0(1-\frac{t}{T})for0\le t<T$

where $R_0=1\Omega ,$ and C = 1 F. We are also given that $T=3R_{0}C$ and the source voltage is $V_s=1V$. If the current at time t = 0 is 1 A. then the current I(t), in amperes, at time t = T/2 is (rounded off to 2 decimal places).

1. 0.25

Figure shows a circuit which has a coil of resistance R and inductance L. At resonance, the Q-factor of the coil is given by

A series R-L-C circuit is excited with a 50 V, 50 Hz sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor $V_L$ is V.

1. 50

For the circuit, shown in the figure, the total real power delivered by the source to the load is kW.

1. 1.866

In the given circuit, the two-port network has the impendance matrix $\left[Z\right]=\left[\begin{array}{cc}40& 60\\ 60& 120\end{array}\right]$. The value of $Z_L$ for which maximum power is transferred to the load is $\Omega$.

1. 48

Find the transformer ratios a and b such that the impedance $\left(Z_{in}\right)$ is resistive and equals $2.5\Omega$ when the network is excited with a sine wave voltage of angular frequency of $5000rad/s$.

A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10 $\Omega$, 5 $\Omega$, 2 $\Omega$ are provided. Consider all possible permutations of the given resistors into the positions A, B, C and identify the configurations with maximum possible overall resisatance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is

1. 2.143

Consider the circuit shown in the figure below, switch is operated at $\tau =0$

The time constant of the given circuit is

1. 7.35

Consider the building block called "Network N" shown in the figure.



Let $C=100\mu F$ and $R=10k\Omega$,



The trasfer function $\frac{V_3\left(s\right)}{V_1\left(s\right)}$ of the cascaded network is

In a series RLC circuit, L = 40 mH is given. If the instantaneous voltage and current are $100\cos (314t-5^{\circ })V$ and $10\cos (314t-{50}^{\circ })A$ respectively, the value of R and C will be

The total power dissipated in the circuit, shown in the figure, is 1 kW.







The voltmeter, across the load, reads 200 V. The value of $K_L$ is

1. 17.332

The steady state output of the circuit shown in the figure is given by

$y\left(t\right)=A\left(\omega \right)sin(\omega t+\varphi (\omega \left)\right)$. If the amplitude $\left|A\right(\omega \left)\right|=0.25$, then the frequency $\omega$ is

1. 0.24

1. 8

In the figure, $Z_1=10\angle -{60}^{\circ }$, $Z_2=10\angle {60}^{\circ }$, $Z_3=50\angle {53.13}^{\circ }$. Thevenin's impedance seen from X-Y is

A balanced abc-sequence Y-connected source with $V_{an}=100\angle {10}^{\circ }$ V is connected to a $\Delta$-connected balanced load with impedence $(8+j4)\Omega$ per phase. Then the line current $I_c$ is

Assume that the circuit in the figure has reached the steady state before time t = 0 when the $3\Omega$ resistor suddenly burns out, resulting in an open circuit. The current i(t) (in ampere) at $t=0^{+}$ is

1. -1

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

In the circuit shown in the figure, the angular frequancy $\omega$ (in rad/s), at which the Norton equivalent impendance as seen from terminals b-b' is purely resistive, is

1. 2

The connection of two 2-port networks is shown in the figure. The ABCD parameters of $N_1$ and $N_2$ networks are given as



${\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]}_{N1}$ = $\left[\begin{array}{cc}1& 5\\ 0& 1\end{array}\right]$



and



${\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]}_{N2}$ = $\left[\begin{array}{cc}1& 0\\ 0.2& 1\end{array}\right]$







The ABCD parameters of the combined 2-port network are

1. 96

In the given circuit, superposition is applied. When $V_2$ is set to 0 V, the current $I_2$ is -6 A. When $V_1$ is set to 0 V, the current $I_1$ is +6 A. Current $I_3$ (in A) when both sources are applied will be (up to two decimal places)

1. 1

1. -420

LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

Two networks are connected in cascade as shown in the figure. With the usual notations the equivalent A,B,C and D constants are obtained. Given that, $C=0.025\angle {45}^o$, the value of $Z_2$ is

Consider the network shown below with $R_1=1\Omega$, $R_2=2\Omega$ and $R_3=3\Omega$. The network is connected to a constant voltage source of 11 V.





The magnitude of the current (in amperes, accurate to two decimal places) through the sources is

1. 8