Five capacitors of capacitances C1 = C2 = C3 = C4 = 10µF and C5 = 2.5µF are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are: ____.
Correct Answer :
5 µF, 125 µC on all capacitors
Solution :
The diagram supplied in the image shows the five capacitors connected to a 50 V battery as follows:
‑ Capacitors C1, C2, C3 and C4 (each 10 µF) are arranged **in series**.
‑ The series string is placed **in parallel** with capacitor C5 (2.5 µF).
Thus the overall circuit consists of a series group of four equal capacitors and a single capacitor that shares the same terminals as that group.
**Step 1: Find the equivalent capacitance of the series group.**
Since C1=C2=C3=C4=10 µF,
**Step 2: Combine with C5 in parallel.**
**Step 3: Determine the voltage across each branch.**
The series group and C5 are in parallel, so they share the full battery voltage:
**Step 4: Find the charge on each capacitor.**
For the parallel capacitor C5:
For the series capacitors (C1–C4):
In a series connection the charge on each capacitor is the same. The voltage across each of the four equal‑capacitance capacitors is one‑fourth of the total branch voltage:
Hence the charge on any Ci (i = 1…4) is
All five capacitors therefore store the same charge of 125 µC.
**Result:** The equivalent capacitance of the network is 5 µF, and each capacitor (C1 through C5) carries a charge of 125 µC, exactly matching the given correct option.
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