Electric Circuits

Question 1
A benchtop dc power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source for all load currents going down to 0 A. When connected to an ideal rheostat, find the load resistance value at which maximum power is transferred, and the corresponding load voltage and current.
A
Short, \infty A, 10 V
B
Open, 4 A, 0 V
C
2.5 \Omega, 4 A, 10 V
D
2.5 \Omega, 4 A, 5 V
GATE EE 2020      Network Theorems
Question 1 Explanation: 



Maximum power transistor of VI product is maximum. If draw the the curve, it intersect (10, 4) that will give maximum power. The terminal voltage is 10 V (Load voltage) and current is 4 A (Load current). Load resistance is \frac{10}{4}=2.5\Omega .
Question 2
The Thevenin equivalent voltage, V_{TH}, in V (rounded off to 2 decimal places) of the network shown below, is _______ .
A
5
B
7
C
14
D
6
GATE EE 2020      Network Theorems
Question 2 Explanation: 
Only voltage source 4V is there and current source 5A is open circuited

From the above circuit,
V_{TH1}=4V

Case-II:
Only current source 5A is there and voltage source 4V is short circuited.

From the above circuit,
V_{TH2}=2 \times 5=10V
By applying superposition theorem,
V_{TH}=V_{TH1}+V_{TH2}=10+4=14V
Question 3
x_R\; and \; x_A are, respectively, the rms and average values of x(t) = x(t - T), and similarly, y_R\; and \; y_A are, respectively, the rms and average values of y(t) = kx(t). k, \;T are independent of t. Which of the following is true?
A
y_A=kx_A;\; y_R=kx_R
B
y_A=kx_A;\; y_R\neq kx_R
C
y_A \neq kx_A;\; y_R= kx_R
D
y_A \neq kx_A;\; y_R\neq kx_R
GATE EE 2020      Network Theorems
Question 3 Explanation: 
Given that,
\begin{aligned} x(t)&=x(t-T) \; \text{ i.e. periodic signal}\\ \text{Average of } x(t)&=x_{A}\\ \text{Rms of }x(t)&=x_{R} \\ \text{Average of }y(t)&=y_{A}\\ \text{Rms of } y(t)&=y_{R} \\ y(t)&=k_{x}(t_{0}) \; \; ....(i) \\ &\text{Using equation(i),}\\ \text{Average of }y(t)&=k \times \text{ Average of }x(t) \\ y_{A}&=kx_{A}\\ \text{Power of }y(t)&=|k|^{2}\text{ Power of }x(t) \\ Rms^{2} \text{ of } y(t)&=|k|^{2}\; Rms^{2}\text{ of }x(t) \\ y_{R}^{2}=|k|^{2}\cdot x_{R}^{2} \\ y_{R}=|k|x_{R}\end{aligned}
Question 4
The current flowing in the circuit shown below in amperes is _____
A
0
B
1
C
2
D
4
GATE EE 2019      Network Theorems
Question 4 Explanation: 


By Millman'e theorem,
E=\frac{\frac{200}{50}+\frac{160}{40}-\frac{100}{25}-\frac{80}{20}}{\frac{1}{50}+\frac{1}{40}+\frac{1}{25}+\frac{1}{20}}=0V
\frac{1}{R}=\frac{1}{50}+\frac{1}{40}+\frac{1}{25}+\frac{1}{20}
Simplified circuit,
\therefore \;\;I=0A
Question 5
A 0.1\mu F capacitor charged to 100 V is discharged through a 1 k\Omega resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1V is ______
A
0.25
B
0.65
C
0.45
D
0.85
GATE EE 2019      Steady state AC Analysis
Question 5 Explanation: 


\begin{aligned} v_c(t)&=V_0e^{-t/\tau } \\ V_0&=100V \\ \tau &=RC=(10^3)(10^{-7}) \\ &=10^{-4}sec \\ \therefore \;v_c(t)&=100e^{-10^4 t }V \end{aligned}
Let the time required by the voltage across the capacitor to drop to 1 V is t_1,
\begin{aligned} \therefore \; v_c(t_1)&=100e^{-10^4t_1} \\ \text{But, } v_c(t_1)&=0 \\ \text{So, }0&=100e^{-10^4t_1} \\ t_1&=0.46msec \end{aligned}
Question 6
The line currents of a three-phase four wire system are square waves with amplitude of 100 A. These three currents are phase shifted by 120^{\circ} with respect to each other. The rms value of neutral current is
A
0 A
B
\frac{100}{\sqrt{3}} A
C
100 A
D
300 A
GATE EE 2019      Magnetically Coupled Circuits, Network Topology and Filters
Question 6 Explanation: 


I_N=I_a+I_b+I_c
(I_N)_{rms}=100A
Question 7
The current I flowing in the circuit shown below in amperes (round off to one decimal place) is ____
A
0.8
B
1.1
C
1.4
D
1.9
GATE EE 2019      Basics
Question 7 Explanation: 


Applying nodal at node x,
-I-2+\frac{V_x-5I}{3}=0
-3I-6+V_x-5I=0
\Rightarrow \; 8I=V_x-6\;\;...(i)
As, I=\frac{20-V_x}{2}
\Rightarrow \; V_x=20-2I\;\;...(ii)
Substituting (ii) in (i),
8I=20-2I-6
10I=14
I=1.4A
Question 8
The voltage v(t) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency \omega=100 radian/s. When the inductor current i(t) is in phase with the voltage v(t), the magnitude of the impedance Z (in \Omega) seen between the terminals a and b is ________ (up to 2 decimal places).
A
25
B
50
C
100
D
150
GATE EE 2018      Resonance and Locus Diagrams
Question 8 Explanation: 
At resonance imaginary part of Z_{eq}=0
Real of Z_{eq}=\frac{R_1 X_c^2}{R_1^2+X-c^2}
\;\;=\frac{100 \times 100 \times 100}{100^2+100^2}=50\Omega
Question 9
The voltage across the circuit in the figure, and the current through it, are given by the following expressions:
v(t) = 5 - 10 cos(\omega t + 60^{\circ}) V
i(t) = 5 + X cos(\omega t) A
where \omega =100 \pi radian/s. If the average power delivered to the circuit is zero, then the value of X (in Ampere) is _____ (up to 2 decimal places).
A
5
B
10
C
15
D
20
GATE EE 2018      Steady State AC Analysis
Question 9 Explanation: 
Given that,
v(t)=5-10 \cos (\omega t+60^{\circ})
i(t)=5+C \cos (\omega t-0^{\circ})
P_{req}=0
0=5 \times 5 +\frac{1}{2}[(-10)(X)\cos(60^{\circ})]
-25=\frac{1}{2}[(-10)(X)\cos(60^{\circ})]
X=10
Question 10
The equivalent impedance Z_{eq} for the infinite ladder circuit shown in the figure is
A
j12 \Omega
B
-j12 \Omega
C
j13 \Omega
D
13 \Omega
GATE EE 2018      Basics
Question 10 Explanation: 




Z_1=j9
Z_2=j5-j1=j4
Z_{eq}=Z_1+\frac{Z_2Z_{eq}}{Z_2+Z_{eq}}
By solving above equation,
Z_{eq}=j12


There are 10 questions to complete.
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