1
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Let $i_C, i_L$, and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens(S). Which one of the following is true?

GATE ECE 2025 Network Theory - Sinusoidal Steady State Response Question 1 English
A
$i_C=0.25 \angle 180^{\circ} \mathrm{A}, \quad i_L=0.1 \angle 0^{\circ} \mathrm{A}, \quad i_R=0.2 \angle 90^{\circ} \mathrm{A}$
B
$i_C=4 \angle 180^{\circ} \mathrm{A}, \quad i_L=10 \angle 0^{\circ} \mathrm{A}, \quad i_R=5 \angle 90^{\circ} \mathrm{A}$
C
$i_C=0.25 \angle 270^{\circ} \mathrm{A}, \quad i_L=0.1 \angle 90^{\circ} \mathrm{A}, \quad i_R=0.2 \angle 90^{\circ} \mathrm{A}$
D
$i_C=4 \angle 90^{\circ} \mathrm{A}, \quad i_L=10 \angle 270^{\circ} \mathrm{A}, \quad i_R=5 \angle 0^{\circ} \mathrm{A}$
2
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t)=100 \cos (200 t)$.

What should be the value of the variable capacitor $C$ such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A , respectively?

GATE ECE 2025 Network Theory - Sinusoidal Steady State Response Question 2 English
A
$25 \mu \mathrm{~F}$
B
$4 \mu \mathrm{~F}$
C
$0.25 \mu \mathrm{~F}$
D
Insufficient information to find $C$
3
GATE ECE 2025
MCQ (Single Correct Answer)
+2
-0.67

The $Z$-parameter matrix of a two port network relates the port voltages and port currents as follows:

$$ \left[\begin{array}{l} V_1 \\ V_2 \end{array}\right]=Z\left[\begin{array}{l} I_1 \\ I_2 \end{array}\right] $$

The Z-parameter matrix (with each entry in Ohms) of the network shown below is

___________.

GATE ECE 2025 Network Theory - Two Port Networks Question 1 English
A
$\left[\begin{array}{cc}\frac{10}{3} & \frac{2}{3} \\ \frac{2}{3} & \frac{10}{3}\end{array}\right]$
B
$\left[\begin{array}{cc}\frac{2}{3} & \frac{10}{3} \\ \frac{10}{3} & \frac{2}{3}\end{array}\right]$
C
$\left[\begin{array}{cc}10 & 2 \\ 2 & 10\end{array}\right]$
D
$\left[\begin{array}{cc}\frac{10}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{10}{3}\end{array}\right]$
4
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_1[n]$ and $h_2[n]$ denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, $\delta[n]$ is the unit impulse, and $b>0$.

Assuming $h_2[n] \neq \delta[n]$, the overall system (denoted by the dashed box) is_________.

GATE ECE 2025 Signals and Systems - Discrete Time Linear Time Invariant Systems Question 1 English
A
linear and time invariant
B
linear and time variant
C
nonlinear and time invariant
D
nonlinear and time variant
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