A capacitor of capacitance `5muF` is charged to a potential difference 200 V and then allowed to dischage through a resistance `1kOmega`. The cahrge on the capacitor at the instant the current through the resistance is 100 Ma, is (in `muC`):

Options

A. (a)50
B. (b)100
C. (c)500
D. (d)1000

Explanation

To solve the problem step by step, we will follow the principles of capacitors and Ohm's law.

### Step 1: Understand the given values
- Capacitance \( C = 5 \mu F = 5 \times 10^{-6} F \)
- Initial potential difference \( V_0 = 200 V \)
- Resistance \( R = 1 k\Omega = 1000 \Omega \)
- Current \( I = 100 mA = 0.1 A \)

### Step 2: Calculate the potential difference across the capacitor when the current is 100 mA
Using Ohm's law, we know that:
\[ V = I \times R \]
Substituting the values:
\[ V = 0.1 A \times 1000 \Omega = 100 V \]

### Step 3: Relate the charge on the capacitor to the potential difference
The charge \( Q \) on the capacitor is given by the formula:
\[ Q = C \times V \]
Substituting the values we have:
\[ Q = 5 \times 10^{-6} F \times 100 V \]

### Step 4: Calculate the charge
Calculating the above expression:
\[ Q = 5 \times 10^{-6} \times 100 = 5 \times 10^{-4} C \]

### Step 5: Convert the charge into microcoulombs
To convert coulombs to microcoulombs:
\[ Q = 5 \times 10^{-4} C = 500 \mu C \]

### Final Answer
The charge on the capacitor at the instant the current through the resistance is 100 mA is **500 µC**.

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