Question

In the given circuit the sliding contact is pulled outwards such that the electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 Ω, the value of the current in the circuit will be          A.

• A. 2 A
• B. 4 A
• C. 3 A
• D. 5 A

Hint:

In RL circuits, the current can be determined using the equation \( \epsilon = L \frac{dI}{dt} + IR \). Make sure to substitute the correct values and solve for the unknown current.

Answer 1

The Correct Option is C

To determine the current in the RL circuit at the given instant:

1. Circuit Equation:
The governing equation is:

\[ V = L\frac{di}{dt} + IR \]
Given values:
- \( V = 12 \) V
- \( L = 3 \) H
- \( R = 12 \) Ω
- \( \frac{di}{dt} = -8 \) A/s (current decreasing)

2. Calculation:
\[ 12 = 3(-8) + I(12) \]
\[ 12 = -24 + 12I \]
\[ 36 = 12I \]
\[ I = 3 \text{ A} \]

The current at this instant is 3 A.