How many percent of work done by a battery is consumed to fully charge a capacitor which is stored as electric potential energy in the capacitor ?

Options

A. 25
B. 50
C. 70
D. 100

Answer

To solve the problem of how many percent of work done by a battery is consumed to fully charge a capacitor, we can follow these steps:

### Step 1: Understand the Work Done by the Battery
The work done by the battery (W) to charge a capacitor is given by the formula:
\[ W = Q \cdot V \]
where \( Q \) is the charge and \( V \) is the voltage of the battery.

### Step 2: Calculate the Potential Energy Stored in the Capacitor
The potential energy (U) stored in a fully charged capacitor is given by:
\[ U = \frac{1}{2} Q \cdot V \]

### Step 3: Determine the Percentage of Work Done Consumed
To find the percentage of work done by the battery that is consumed in charging the capacitor, we can use the formula:
\[ \text{Percentage} = \left( \frac{U}{W} \right) \times 100 \]

Substituting the expressions for \( U \) and \( W \):
\[ \text{Percentage} = \left( \frac{\frac{1}{2} Q \cdot V}{Q \cdot V} \right) \times 100 \]

### Step 4: Simplify the Expression
The \( Q \cdot V \) terms cancel out:
\[ \text{Percentage} = \left( \frac{\frac{1}{2}}{1} \right) \times 100 = \frac{1}{2} \times 100 = 50\% \]

### Conclusion
Thus, 50% of the work done by the battery is consumed to fully charge the capacitor, which is stored as electric potential energy in the capacitor.

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