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 \gtPower 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.
Question 6
A single-phase transformer is to be switched to the supply to have minimum inrush current. The switch should be closed at
A
maximum supply voltage
B
zero supply voltage
C
\frac{1}{\sqrt{2}} maximum supply voltage
D
1/2 maximum supply voltage
Electrical Machines   Transformers
Question 6 Explanation: 
When the value of input voltage is maximum, rate of change of core flux is minimum, as both are 90^{\circ} out of phase in case of sinusoidal input.
Question 7
It is desirable to eliminate 5th harmonic voltage from the phase voltage of an alternator. The coils should be short-pitched by an electrical angle of
A
30^{\circ}
B
36^{\circ}
C
72^{\circ}
D
18^{\circ}
Electrical Machines   Synchronous Machines
Question 7 Explanation: 
For fifth harmonics, 5\beta =180^{\circ}
\Rightarrow \;\;\beta =36^{\circ}
Question 8
Figure shows the magnetization curves of an alternator at rated armature current, unity power factor and also at no load. The magnetization curve for rated armature current, 0.8 power factor leading is given by
A
curve A
B
curve B
C
curve C
D
curve D
Electrical Machines   Synchronous Machines
Question 9
The core flux of a practical transformer with a resistive load
A
is strictly constant with load changes
B
increases linearly with load
C
increases as the square root of the load
D
decreases with increased load
Electrical Machines   Transformers
Question 10
X_{d} , {X}'_{d} and {X}''_{d} are steady state d-axis synchronous reactance, transient d-axis reactance and sub-transient d-axis reactance of a synchronous machine respectively. Which of the following statements is true?
A
X_{d} \gt {X}'_{d} \gt {X}"_{d}
B
{X}''_{d} \gt {X}'_{d} \gt X_{d}
C
{X}'_{d} \gt {X}''_{d} \gt X_{d}
D
X_{d} \gt {X}''_{d} \gt {X}'_{d}
Electrical Machines   Synchronous Machines
There are 10 questions to complete.