A condenser charged to a potential of 200 V, has the energy of 1 joule. The capacity of the condenser is

Options

A. `25muF`
B. `50muF`
C. `75muF`
D. `30muF`

Explanation

To find the capacity of the condenser, we can use the formula for the energy stored in a capacitor, which is given by:

\[ E = \frac{1}{2} C V^2 \]

Where:
- \( E \) is the energy stored in the capacitor (in joules),
- \( C \) is the capacitance (in farads),
- \( V \) is the potential difference across the capacitor (in volts).

Given:
- \( E = 1 \) joule,
- \( V = 200 \) volts.

We need to find the capacitance \( C \).

### Step 1: Rearranging the formula
We can rearrange the formula to solve for \( C \):

\[ C = \frac{2E}{V^2} \]

### Step 2: Substituting the values
Now, we substitute the known values into the equation:

\[ C = \frac{2 \times 1 \text{ joule}}{(200 \text{ volts})^2} \]

### Step 3: Calculating \( V^2 \)
Calculate \( V^2 \):

\[ V^2 = 200^2 = 40000 \text{ volts}^2 \]

### Step 4: Substituting \( V^2 \) back into the equation
Now substitute \( V^2 \) back into the equation for \( C \):

\[ C = \frac{2 \times 1}{40000} \]

### Step 5: Performing the calculation
Now perform the calculation:

\[ C = \frac{2}{40000} = \frac{1}{20000} \]

### Step 6: Converting to microfarads
Since \( 1 \text{ farad} = 10^6 \text{ microfarads} \):

\[ C = \frac{1}{20000} \text{ farads} = \frac{1 \times 10^6}{20000} \text{ microfarads} = 50 \text{ microfarads} \]

### Final Answer
Thus, the capacity of the condenser is:

\[ C = 50 \text{ microfarads} \]

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