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

Step 1: Understanding the Concept:
Self-inductance is the property of a coil by which an EMF is induced in it when the current through it changes. The magnitude of this induced EMF is proportional to the rate of change of current.
Step 2: Key Formula or Approach:
The induced EMF ($e$) is given by: \[ e = L \left| \frac{dI}{dt} \right| \] Where $L$ is the self-inductance, $dI$ is the change in current, and $dt$ is the time interval.
Step 3: Detailed Explanation:
Given values: \[ e = 20 \text{ V} \] \[ dI = 4\text{ A} - 2\text{ A} = 2\text{ A} \] \[ dt = 0.1 \text{ s} \] Plugging these into the formula: \[ 20 = L \left( \frac{2}{0.1} \right) \] \[ 20 = L \times 20 \] \[ L = \frac{20}{20} = 1 \text{ H} \]
Step 4: Final Answer:
The self-inductance of the coil is 1 H.