Consider three capacitors C 1 , C 2 , and C 3 and a battery. If only C 1 is conn

Question

Consider three capacitors C1, C2, and C3 and a battery. If only C1 is connected to the battery, the charge on C1 is 31.0 µC. Now C1 is disconnected, discharged, and connected in series with C2. When the series combination of C2 and C1 is connected across the battery, the charge on C1 is 22.4 µC. The circuit is disconnected, and both capacitors are discharged. Next, C3, C1, and the battery are connected in series, resulting in a charge on C1 of 25.0 µC. If, after being disconnected and discharged, C1, C2, and C3 are connected in series with one another and with the battery, what is the charge on C1?

Explanation / Answer

1)

Consider three capacitors C1, C2, C3, and a battery. If C1 is connected to the battery, the charge on C1 is 31 microCoulombs. Now C1 is disconnected, discharged, and connected in series with C2.

2)

When the series combination of C2 and C1 is connected across the battery,
the charge on C1 is 22.4 microCoulombs. The circuit is disconnected and the capacitors discharged.

3)

Capacitor C3, capacitor C1, and the battery are connected in series, resulting in a charge on C1 of 25
microCoulombs. If, after being disconnected and discharged,

4)

C1, C2, and C3 are connected in series with one another and with the battery,
what is the exact charge (in microCoulombs) on C1?


V = battery
part 1 gives us 31µC = C1V

Part 2
equiv C = C1C2/(C1+C2)
22.4µC = VC1C2/(C1+C2)

part 3
equiv C = C1C3/(C1+C3)
25µC = VC1C3/(C1+C3)

part 4
equiv Cq = 1[1/C1 + 1/C2 + 1/C3]
Q = Cq x V ( voltage is not given)

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