Question

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

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

Hint:

Self-inductance measures the opposition of a coil to change in current. Use the formula \[ E = L\frac{di}{dt} \] where \(\frac{di}{dt}\) is the rate of change of current.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem involves Faraday's Law of Induction applied to self-inductance, where a changing current induces an electromotive force (EMF) in the same coil.
Step 2: Key Formula or Approach:
The magnitude of induced EMF (\(E\)) is given by:
\[ E = L \left| \frac{di}{dt} \right| \]
where \(L\) is the self-inductance and \(\frac{di}{dt}\) is the rate of change of current.
Step 3: Detailed Explanation:
Given:
Initial current, \(i_1 = 2 \, A\)
Final current, \(i_2 = 4 \, A\)
Change in current, \(\Delta i = 4 - 2 = 2 \, A\)
Time taken, \(\Delta t = 0.1 \, s\)
Induced EMF, \(E = 20 \, V\)
Using the formula:
\[ 20 = L \times \frac{2}{0.1} \]
\[ 20 = L \times 20 \]
\[ L = 1 \, H \]
Step 4: Final Answer:
The self-inductance of the coil is \(1 \, H\).