Question

In a series combination of capacitors connected across a battery

• A. each capacitor has an equal charge for certain values of capacitances only
• B. each capacitor has different charge for a certain value of its capacitance
• C. each capacitor has equal charge for any value of its capacitance
• D. each capacitor has different charge for any value of its capacitance

Hint:

Remember the key rules for combinations: - Series: Same Charge (Q), Different Voltage (V). \(1/C_{eq} = 1/C_1 + 1/C_2 + ...\) - Parallel: Same Voltage (V), Different Charge (Q). \(C_{eq} = C_1 + C_2 + ...\)

Answer 1

The Correct Option is C

Step 1: Concept Overview:
Capacitors in series are connected sequentially, creating a single route for charge movement.

Step 3: Explanation:
When a battery is connected to series capacitors, it applies a charge +Q to the initial plate of the first capacitor. This induces a -Q charge on the adjacent plate of the same capacitor. The +Q charge from this plate is then transferred to the first plate of the subsequent capacitor. This charge transfer continues throughout the series. Consequently, each capacitor plate accumulates the same magnitude of charge, Q. This is due to charge conservation and the singular pathway for charge flow. This principle applies irrespective of the individual capacitance values. While the voltage across each capacitor may vary (unless capacitances are identical), the charge on each remains constant.

Step 4: Conclusion:
In a series arrangement, every capacitor holds the same charge, regardless of its specific capacitance value.