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.