# GATE EE 2001

 Question 1
In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor
 A is always zero B can never be greater than the input voltage C can be greater than the input voltage, however, it is $90^{\circ}$ out of phase with the input voltage D can be greater than the input voltage, and is in phase with the input voltage.
Electric Circuits   Resonance and Locus Diagrams
Question 1 Explanation:
In a series RLC circuit, at resonance
$V_L=jQV_{source}$ and $V_c=-jQV_{source}$
also for $Q \gt 1, |V_c| \gt |V_{source}|$
Hence, option (C) is correct.
 Question 2
Two incandescent light bulbs of 40 W and 60 W rating are connected in series across the mains. Then
 A the bulbs together consume 100 W B the bulbs together consume 50W C the 60 W bulb glows brighter D the 40 W bulb glows brighter
Electric Circuits   Basics
Question 2 Explanation:
$\because \;\;P\propto \frac{1}{R}$
Therefore , resistance of 40 W bulb $\gt$ resistance of 60 W bulb.
For series connection, current through both the bulbs will be same $P=I^2R$ (for series connection).
Power consumed by 40 W bulb $\gt$Power consumed by 60 W bulb.
Hencem the 40 W bulb glows brighter.

 Question 3
A unit step voltage is applied at t = 0 to a series RL circuit with zero initial conditions.
 A It is possible for the current to be oscillatory. B The voltage across the resistor at t = $0^{+}$ is zero. C The energy stored in the inductor in the steady state is zero. D The resistor current eventually falls to zero.
Electric Circuits   Transients and Steady State Response
Question 3 Explanation:
At $t=0^+$ inductor works as open circuit. Hence, complete source voltage drops across it and consequently, current through the resistor R is zero. Hence, voltage across the resistor at $t=0^+$ is zero. And further with time it rises accroding to $V_R(t)=(1-e^{-Rt/L})u(t)$. Question 4
Given two coupled inductors $L_{1}$ and $L_{2}$, their mutual inductance M satisfies
 A $M=\sqrt{L^{2}_{1}+L^{2}_{2}}$ B $M \gt \frac{\left ( L_{1}+L_{2} \right )}{2}$ C $M\gt \sqrt{L_{1}L_{2}}$ D $M\leq \sqrt{L_{1}L_{2}}$
Electric Circuits   Magnetically Coupled Circuits, Network Topology and Filters
Question 4 Explanation:
$M=K\sqrt{L_1L_2}$
where , K= coefficient of coupling
$\because \; 0 \lt K \lt 1$
$\therefore \; M \leq \sqrt{L_1L_2}$
 Question 5
A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer
 A higher voltage B lower impedance C greater power D better regulation
Electric Circuits   Two Port Network and Network Functions
Question 5 Explanation:
For a passive two port network, output powe can never be grater than input power.

There are 5 questions to complete.