GATE EC Circuit Analysis questions

The number of independent loops for a network with $n$ nodes and $b$ branches is

In the given figure, $A_{1}, A_{2}$ and $A_{3}$ are ideal ammeters. If $\mathrm{A}_{2}$ and $\mathrm{A}_{3}$ read $3 \mathrm{~A}$ and $4 \mathrm{~A}$ respectvely, then $A_{1}$ should read

The voltages $\mathrm{V}_{\mathrm{C} 1}, \mathrm{~V}_{\mathrm{C} 2}$, and $\mathrm{V}_{\mathrm{C} 3}$ across the capacitors in the circuit in the given figure, under steady state, are respectively.

The current, $\text{i(t)}$, through a $10 \; \Omega$ resistor in series with an inductance, is given by $i(t)=3+4 \sin \left(100 t+45^{\circ}\right)+4 \sin \left(300 t+60^{\circ}\right)$ Amperes The $\text{RMS}$ value of the current and the power dissipated in the circuit are :

The value of the resistance, $R$, connected across the terminals, $A$ and $B$, which will absorb the maximum power, is

Two $2 \; \mathrm{H}$ inductance coils are connected in series and are also magnetically coupled to each other the coefficient of coupling being $0.1$. The total inductance of the combination can be

Consider a $\text{DC}$ voltage source connected to a series $\mathrm{R}-\mathrm{C}$ circuit. When the steady-state reaches, the ratio of the energy stored in the capacitor to the total energy supplied by the voltage source, is equal to

A $\text{DC}$ voltage source is connected across a series $\text{R-L-C}$ circuit. Under steady-state conditions, the applied $\text{DC}$ voltage drops entirely across the

A ramp voltage, $v(t)=100$ volts, is applied to an $R C$ differentiating circuit with $R=5 \; \mathrm{k} \Omega$ and $C=4$ $\mu \mathrm{F}$. The maximum output voltage is

A series $\text{LCR}$ circuit consisting of $R=10 \; \Omega$, $\left|X_{L}\right|=20 \; \Omega$ and $\left|X_{C}\right|=20 \; \Omega$, is connected across an $a . c$. supply of $200 \text{V rms}$ . The $\text{rms}$ voltage across the capacitor is

The Laplace transform of a unit ramp function starting at $t=a$, is

In the figure is $\mathrm{A}^{1} \mathrm{~A}^{2}$ and $\mathrm{A}^{3}$ are ideal ammeters. If $\mathrm{A}^{1}$ reads $5 \mathrm{A}, \mathrm{~A}^{2}$ reads $12 \mathrm{A}$, then $\mathrm{A}^{3}$ should read.

The two electrical sub network $N^{1}$ and $N^{2}$ are connected through three resistors as shown in the figure. The voltage across $5 \; \mathrm{ohm}$ resistor and $1 \; \mathrm{ohm}$ resistor are given to be $10 \mathrm{~V}$ and $5 \mathrm{~V}$, respectively. Then voltage across $15 \; \mathrm{ohm}$ resistor is

A network contains linear resistors and ideal voltage sources. If values of all the resistors are doubled, then the voltage across each resistor is

Of the four networks, $\mathrm{N}_{1}, \mathrm{~N}_{2}, \mathrm{~N}_{3}$ and $\mathrm{N}_{4}$ of the given figure, the networks having identical driving point functions are

For the compensated attenuator of the given figure, the impulse response under the condition $R_{1} C_{1} = R_{2} C_{2}$ is

For a $2$-port network to be reciprocal,

Relative to a given fixed tree of a network,