# Objective Questions on Circuit Theory | 10

1. Consider the following circuit :
Switch is closed at t = 0
Find i(0 +)

At t = 0, capacitor will be short.
So i(0) = V / R.

2. In question no. 1, which of the following is true ?

At t = 0+, capacitor will be short.
So, i(0) = ic = V/R.

3. The impulse response of the system described by the differential equation
$\frac {dy} {dx} + 6y = x(t)$
will be

Under Construction.

4. The current at a given point in certain circuit is given as function of time as
i(t) = d – 3+t, t = 99 sec & t = 102 sec is

$\frac {dq} {dt} = I$
$\rightarrow \; dq = I.dt$
$\rightarrow \; Q= \int_{99}^{102}I.dt$.

5. What would be the power given by source V2 ?

Among two voltage source, only 10V source will deliver power to 5 V voltage source. Power given by V2 = – V2 / R = - 5 W.

6. Two combination of similar inductors are show below. Which one has more inductance between A & B

Here in circuit B, mutual inductance is additive. So in circuit 2 has more inductance.

7. Consider the following circuit. What is the value of i ?

Voltage source will offer zero resistance path to current. So net current in 1 Ω resistance depends only voltage source. So current i = 5 × i = 5 A.

8. In above question, power given in the SV source is

Source current = 5 – 1 = 4 Amp.
Power given by the 5 V source = 5 × 4 = 20 W.

9. Total power consumed in the circuit below is 10 W. Find x.

Total power consumed = x2× 2 + 22/2
⇒ 10 W = 2 ×x2 + 2
Therefore, x = 2 A.

10. If Vout = 1V for 1 KHz input then what would be Vout for 10 KHz for same input ?

$Transfer \; function \; = \;\frac {1} {10^{-6}s + 1}$
So a frequency of 1 MHz, the gain is 1 or 0 dB.

11. A battery of E volts is supplying a steady current to a series circuit of total resistance R ohm & inductance L Henry. A part R1 of the total resistance is suddenly short circuited.
Find the expression for current flowing through the battery subsequent to the operation

Let, after t sec, the current is i.
$(R\;-\;R_1)i\;+\;L\frac{di}{dt}= E$
$\Rightarrow \;i\;=\;Ke^{-\frac{R\;-\;R_1}{L}t\;+\;\frac{E}{R\;-\;R_1}}$
At t = 0, i = E / R,
$Then,\;K\;=\;\frac{E}{R}\;-\;\frac{E}{R\;–\;R_1}$.

12. In above question, determine the current if E = 100 V, R = 20 ohm, R1 = 10 Ohm & L = 2 H at 0.5 sec after short circuit

$= \frac {E}{R\;–\;R_1}\left[\;1\;-\;\frac{R-1}{R}\;\times \;e^{-\;\frac{R\;–\;R_1}{L}t}\right]$.

13. A first order linear system is initially relaxed. For a unit step signal u(t), the response (1 – e - 3t ) for t > 0. If the signal 3u(t) + δ (T) is applied to same initially relaxed system, the response will be

Using the principal of superposition so output due to 3u(t) + δ(t) is
= 3 – 3e – 3t + 3e –3t
= 3 = 3u(t) .

14. A 10 V battery with an internal resistance of 1 Ω is connected across a non-linear load whose V. I characteristic are 7i = V2 + 2V. The current delivered by the battery is

Voltage across the non linear load = 10 – 1× I
So, 7I = V2 + 2V
I = 5A.

15. Find the total power absorbed by the resistor in the given circuit.

Equivalent circuit can be drawn,
P = I2R.

16. In the circuit shown below if I = 2A then find V ?

The circuit can be redrawn as
⇒ V = ½ × 2 + ½ × 2 =2 V.

17. What is I1 in the given circuit ?

Voltage across 2 ohm resistance carrying current I1 is
= (6 × 1) / 4 + (3 × 1) / 3 = 3V.

18. What is Va in the below circuit

Applying superposition theorem,
$V_a = \left (\frac {3R}{2R}\right) \ times 2 R + \frac {5 \ times 2R} {3R} = 2R + \frac {10| {3} = \left (\frac {6R + 10}{3} \ right)$.

19. If L & C both are doubled than damping in above circuit will be

$Damping\; ratio, \; z = \frac{R}{2} \sqrt {\frac {C}{L}}$
Here if L & C both are doubled that means
$Damping\; ratio,\; Z_{new} = \frac{R}{2} \sqrt {\frac {2C}{2L}} = \frac {R}{2} \sqrt {\frac {C} {L}} = Z$.

20. A capacitor is charged by a constant 10mA current sources which is turned on for 1 second. Assuming the capacitor is initially charge free; determine the charge delivered to & the power supplied by the source if the capacitor has a value of 1mF

: V = q / C \$amp; q = i.t
Power delivered P =Vi = qi / C.
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