An inductor L is allowed to discharge through capacitor C. The emf induced across the inductance when the capacitor is fully charged is

Options

A. a.maximum
B. b.minimum
C. c.zero
D. d.infinite

Answer

To solve the problem regarding the induced EMF across an inductor when a capacitor is fully charged, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit**: We have an inductor (L) and a capacitor (C) connected in a circuit. Initially, the capacitor is charged, and we want to analyze the situation when the capacitor is fully charged.

2. **Induced EMF Formula**: The induced EMF (E) across an inductor is given by the formula:
\[ E = -L \frac{dI}{dt} \]
where \(L\) is the inductance and \(\frac{dI}{dt}\) is the rate of change of current through the inductor.

3. **Condition of Fully Charged Capacitor**: When the capacitor is fully charged, it means that it has reached its maximum voltage and no more current is flowing through the circuit. Thus, the current (I) is constant at this point.

4. **Rate of Change of Current**: Since the current is constant when the capacitor is fully charged, the rate of change of current \(\frac{dI}{dt}\) becomes zero:
\[ \frac{dI}{dt} = 0 \]

5. **Calculate Induced EMF**: Substituting \(\frac{dI}{dt} = 0\) into the induced EMF formula:
\[ E = -L \cdot 0 = 0 \]

6. **Conclusion**: Therefore, the induced EMF across the inductor when the capacitor is fully charged is zero.

### Final Answer:
The induced EMF across the inductor when the capacitor is fully charged is **zero**.

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