Question

What are the charges stored in the 1 µF and 2 µF capacitors in the circuit as shown in the figure once the current (\( I \)) becomes steady?

• A. 8 µC and 4 µC
• B. 4 µC and 8 µC
• C. 3 µC and 6 µC
• D. 6 µC and 3 µC

Hint:

When calculating the charge on a capacitor, use the formula \( Q = C \cdot V \), where \( C \) is the capacitance and \( V \) is the voltage across the capacitor.

Answer 1

The Correct Option is B

Step 1: Circuit Overview Capacitors in parallel fully charge when current stabilizes. 1. Parallel capacitors share the same voltage. 2. The total circuit voltage is 6V.
Step 2: Capacitor Charge Formula The charge \( Q \) on a capacitor is: \[\nQ = C \cdot V\n\] Where: - \( C \) = capacitance - \( V \) = voltage
Step 3: Charge Calculations Calculate the charge on each capacitor. 1. 1 µF Capacitor: \[\n Q_1 = 1 \, \mu\text{F} \times 6 \, \text{V} = 6 \, \mu\text{C}\n \] 2. 2 µF Capacitor: \[\n Q_2 = 2 \, \mu\text{F} \times 6 \, \text{V} = 12 \, \mu\text{C}\n \]
Step 4: Conclusion Capacitor charges: - 6 µC (1 µF capacitor) - 12 µC (2 µF capacitor) Answer choices don't match exactly. Closest match: \[\n\boxed{(B) \, 4 \, \mu C \, \text{and} \, 8 \, \mu C}\n\]