A capacitor is connected to a dc voltage source. If another capacitor of same value is connected in series, what happens to the charge stored in the first capacitor?
A capacitor is connected to a dc voltage source. If another capacitor of same value is connected in series, what happens to the charge stored in the first capacitor?
Right Answer is:
Becomes half
SOLUTION
Initial Condition:
- When a single capacitor is connected to a DC source, it charges to a voltage V and stores a charge Q given by:
Q = C * V.
Connecting a Second Capacitor in Series:
- Adding a second capacitor of the same capacitance C in series reduces the total capacitance to
1/Ctotal = 1/C + 1/C = C/2.
- The total voltage across the series combination remains the same (V).
- The charge on each capacitor in the series combination is equal and given by
Qseries = (C/2) * V.
Comparison of Charges:
- Comparing the initial charge Q = C * V with the new charge Qseries = (C/2) * V, we see that the charge on each capacitor in the series combination is half of the original charge.
Key Takeaway:
When a second capacitor of the same capacitance is connected in series with the first capacitor, the total capacitance decreases, and as a result, the charge stored on each capacitor also decreases. This is because the total voltage across the series combination remains constant, but it is now shared between two capacitors.
Additional Insights:
- In a series connection, the voltage across each capacitor is inversely proportional to its capacitance.
- The total capacitance of capacitors in series is always less than the capacitance of the smallest individual capacitor.
- This concept is important in understanding the behavior of capacitors in various circuits, especially in filter circuits and timing circuits.