Two parallel plate condensers of capacity `20 mF` and `30 mF` are charged to the potentials of 30 V and respectively. If likely charged plates are conneted together then the common potential difference be

Options

A. 100 V
B. 50 V
C. 24 V
D. 10 V

Answer

To solve the problem, we need to find the common potential difference when two capacitors are connected together after being charged to different potentials. Here’s a step-by-step solution:

### Step 1: Identify the given values
We have two capacitors:
- Capacitor 1 (C1) = 20 mF (milliFarads) = 20 × 10^-3 F
- Capacitor 2 (C2) = 30 mF (milliFarads) = 30 × 10^-3 F
- Voltage across Capacitor 1 (V1) = 30 V
- Voltage across Capacitor 2 (V2) = 20 V

### Step 2: Calculate the charge on each capacitor
The charge (Q) on a capacitor is given by the formula:
\[ Q = C \times V \]

For Capacitor 1:
\[ Q_1 = C_1 \times V_1 = (20 \times 10^{-3} \, \text{F}) \times (30 \, \text{V}) = 600 \times 10^{-3} \, \text{C} = 0.6 \, \text{C} \]

For Capacitor 2:
\[ Q_2 = C_2 \times V_2 = (30 \times 10^{-3} \, \text{F}) \times (20 \, \text{V}) = 600 \times 10^{-3} \, \text{C} = 0.6 \, \text{C} \]

### Step 3: Determine the total charge
When the like-charged plates are connected together, the total charge (Q_total) is the sum of the charges on both capacitors:
\[ Q_{\text{total}} = Q_1 + Q_2 = 0.6 \, \text{C} + 0.6 \, \text{C} = 1.2 \, \text{C} \]

### Step 4: Calculate the total capacitance
Since the capacitors are connected in parallel, the total capacitance (C_total) is the sum of the individual capacitances:
\[ C_{\text{total}} = C_1 + C_2 = (20 \times 10^{-3} \, \text{F}) + (30 \times 10^{-3} \, \text{F}) = 50 \times 10^{-3} \, \text{F} = 0.05 \, \text{F} \]

### Step 5: Calculate the common potential difference
The common potential difference (V_common) across the combined capacitors can be calculated using the formula:
\[ V_{\text{common}} = \frac{Q_{\text{total}}}{C_{\text{total}}} \]

Substituting the values we found:
\[ V_{\text{common}} = \frac{1.2 \, \text{C}}{0.05 \, \text{F}} = 24 \, \text{V} \]

### Final Answer
The common potential difference when the like-charged plates are connected together is **24 V**.

---