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Network Elements and the Concept of Circuit

  1. Initial voltage on capacitor V0 as marked | V0 | = 5 V. Vs = 8 u(t), where u(t) is the unit step. The voltage marked V at t = 0+ is given by—


    1. 1 V
    2. – 1 V
    3. 13
      V
      3
    4. -
      13
      V
      3
Correct Option: C

If we consider the circuit carefully we see that there are two voltage source present in the circuit and if we have to calculate the net voltage in a particular resistance it can be easily calculated by using superposition theorem.
Case I. When Vs = 8u (t) = 8 V source is treated, the equivalent circuit becomes.
Apply voltage divides method, we get

I =
V
=
8
8
=
16
amp
Req1 + 1 || 11 + (1 / 2)3


I 1 = 16 3 × 1 2 = 8 3 amp
Case II. When | V0 | = 5 V source is treated, the equivalent circuit becomes.
I′ 2 =
V
=
5

Req1 + 1 || 1

=
5
=
10
amp.
1 + (1 / 2)3


I′ 1 = I′2 ×
1
=
10
x
1

1 + 132


I′ 1 =
5
amp.
3

The net current in 1 Ω resistance

= I1 + I′ 1 =
8
+
5
=
13
amp.
333


Voltage drop across 1 Ω =
13
x 1 =
13
V
33



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