Question

If the current in a coil changes from \(2\,\text{A}\) to \(4\,\text{A}\) in \(0.1\,\text{s}\), inducing an EMF of \(20\,\text{V}\), find the self-inductance.

• A. \(0.5\,\text{H}\)
• B. \(1\,\text{H}\)
• C. \(2\,\text{H}\)
• D. \(4\,\text{H}\)

Hint:

Self-inductance problems usually use the formula \( e = L \frac{di}{dt} \). Always compute the rate of change of current first before solving for \(L\).

Answer 1

The Correct Option is B

Concept: Self-inductance is defined using the relation between induced EMF and the rate of change of current: \[ e = L\frac{di}{dt} \] where \(e\) = induced EMF, \(L\) = self-inductance of the coil, \(\frac{di}{dt}\) = rate of change of current.

Step 1: Compute the rate of change of current. The current changes from \(2\,\text{A}\) to \(4\,\text{A}\). \[ \frac{di}{dt} = \frac{4-2}{0.1} \] \[ \frac{di}{dt} = \frac{2}{0.1} = 20 \]

Step 2: Substitute into the self-inductance formula. \[ e = L\frac{di}{dt} \] \[ 20 = L(20) \]

Step 3: Solve for \(L\). \[ L = 1\,\text{H} \]