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.
If the current in a coil changes from \(2A\) to \(4A\) in \(0.1\,s\), inducing an EMF of \(20V\), find the self-inductance.
Show 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.
Updated On: Apr 30, 2026
- \(0.5\,H\)
- \(1\,H\)
- \(2\,H\)
- \(4\,H\)
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The Correct Option is B
Solution and Explanation
Concept:
The induced EMF in an inductor is given by the relation
\[
E = L\frac{di}{dt}
\]
where
\(E\) = induced EMF,
\(L\) = self-inductance,
\(\frac{di}{dt}\) = rate of change of current.
Step 1: Write the given values. Initial current \(i_1 = 2A\) Final current \(i_2 = 4A\) Time interval \[ dt = 0.1\,s \] Induced EMF \[ E = 20V \]
Step 2: Find the rate of change of current. \[ \frac{di}{dt} = \frac{4 - 2}{0.1} \] \[ \frac{di}{dt} = \frac{2}{0.1} = 20 \]
Step 3: Substitute into the EMF formula. \[ E = L\frac{di}{dt} \] \[ 20 = L(20) \] \[ L = 1\,H \]
Step 1: Write the given values. Initial current \(i_1 = 2A\) Final current \(i_2 = 4A\) Time interval \[ dt = 0.1\,s \] Induced EMF \[ E = 20V \]
Step 2: Find the rate of change of current. \[ \frac{di}{dt} = \frac{4 - 2}{0.1} \] \[ \frac{di}{dt} = \frac{2}{0.1} = 20 \]
Step 3: Substitute into the EMF formula. \[ E = L\frac{di}{dt} \] \[ 20 = L(20) \] \[ L = 1\,H \]
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