Network Theory 2024 — MAKAUT · EC-304 · Mid Sem PYQ with solutions

[Figure: A circuit with a 10V DC source. The positive terminal connects to a $2\Omega$ resistor, which then connects to terminal A. Terminal B connects to the negative terminal of the 10V source. A $12\Omega$ resistor is connected between A and B. A $24\Omega$ resistor is also connected between A and B.]

[Figure: A circuit with three nodes $V_1, V_2, V_3$ and a bottom ground rail.

• Far left: A 5A independent current source points up from ground to $V_1$.
• Between $V_1$ and ground: a $2\Omega$ resistor.
• Between $V_1$ and $V_2$: a $1\Omega$ resistor.
• Between $V_2$ and ground: A branch with node label (2) and a $2\Omega$ resistor in series.
• Between $V_2$ and $V_3$: a 20V independent voltage source with positive terminal at $V_2$ and negative at $V_3$.
• Between $V_3$ and ground: A branch containing a $3\Omega$ resistor in series with a 10V independent voltage source (positive terminal up).]

[Figure: A piecewise constant signal $g(t)$ plotted against $t$. The y-axis shows amplitude values $1/2$ and $-1/2$. The signal is $0$ for $t < -2$. It steps up to $1/2$ from $t = -2$ to $t = 2$. At $t = 2$, it steps down to $-1/2$ and remains at $-1/2$ until $t = 4$. For $t > 4$, the signal is $0$.]

[Figure: A staircase-like signal plotted against $t$. An exponential decay envelope $f(t) = e^{-t/2}$ is shown as a dashed line. The signal consists of rectangular pulses of width 1. The first pulse starts at $t=0$ and ends at $t=1$, with its flat top meeting the envelope at $t=0$ (height = 1). The second pulse is from $t=1$ to $t=2$, with its height meeting the envelope at $t=1$ (height = $e^{-1/2}$). This pattern continues infinitely.]

[Figure: A full-wave rectified sine wave $v(t)$ plotted against $t$. The signal starts at 0, peaks at $V_m$, and reaches 0 at $T/2$. The second identical arch spans from $T/2$ to $T$, the third from $T$ to $3T/2$, and so on. The waveform is periodic with a period of $T/2$.]

• (i)
  resonant frequency,
• (ii)
  value of R, L and C,
• (iii)
  quality factor at resonant frequency.

[Figure: A circuit with a 4V DC voltage source. The positive terminal goes through a switch S (marked t=0) to a $2\Omega$ resistor, then to a node. From this node, a $2\Omega$ resistor goes to ground. Also from this node, a $1/2\text{H}$ inductor (with current $i_L(t)$ pointing right) connects to a $1\text{F}$ capacitor. The capacitor goes to ground, with voltage $v_C(t)$ across it (+ on top).]

[Figure: A circuit with a SPDT switch. Position 1 connects to the positive terminal of a 50V DC source. Position 2 connects to the positive terminal of a 10V DC source. The common pole of the switch connects to a series combination of a $40\Omega$ resistor and a $20\text{H}$ inductor. The current $i$ is defined flowing through this series branch back to the common negative return.]

[Figure: A circuit with a $10\text{V}$ independent voltage source (+ on top) in series with a $5\Omega$ resistor on the left. A dependent current source points UP in the middle branch with a value of $0.1 V_x$. The top wire connects these to an $8\Omega$ resistor, which then goes to node A. A $14\Omega$ resistor connects node A to the bottom return rail at node B. The voltage across the $14\Omega$ resistor is labeled $V_x$ (+ at A, - at B).]