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: Understanding the Concept:
When capacitors are connected in series, they are connected end-to-end, forming a single path for the charge to flow.

Step 3: Detailed Explanation:
When a battery is connected across a series combination of capacitors, the battery supplies a charge +Q to the first plate of the first capacitor. This induces a charge -Q on the second plate of the first capacitor. The positive charge +Q from this second plate is repelled and flows to the first plate of the second capacitor. This process continues down the line. As a result, the charge that accumulates on each capacitor plate has the same magnitude, Q. This occurs because charge is conserved, and there is only one path for the charge to flow. This principle holds true regardless of the individual capacitance values of the capacitors in the series. The voltage across each capacitor will be different (unless they have the same capacitance), but the charge on each is the same.

Step 4: Final Answer:
In a series combination, each capacitor has an equal charge for any value of its capacitance.