關於series capacitor 問題

用戶199712

2014-04-27 1:08 am

Two capacitors of capacitance 1 F and 2 F are connected in series to a 100 V supply.

a. Calculate the charge on each capacitor.
b.Without discharging the capacitors, they are disconnected from the supply and connected in parallei so that those plates having the same charge. What is the potential difference across the capacitors?

回答 (1)

天同

2014-04-27 1:40 am

✔ 最佳答案

(a) Let Q be the charge on each capacitor (note that both capacitor carry the same charge Q because they are connected in series), and V1 and V2 be the voltage across the 1-F and 2-F capacitor respectively.

Hence, 100 = V1 + V2
i.e. V2 = 100 - V1

Q = 1 x (V1) = 2 x (V2)
i.e. V1 = 2.(100 - V1)
V1 = 200/3 v = 66.67 v
Therefore Q = 66.67 C

(b) I suppose the capacitors are connected with plates of the same charges be connected together.

Becuase the voltages across each capacitor are the same,
hence, voltage = charge/capacitance = Q1/1 = Q2/2
where Q1 and Q2 are the new charges on the 1-F and 2-F capacitors respectively.
i.e. 2(Q1) = Q2

Since Q1 + Q2 = 2 x 66.67
we have, Q1 + 2(Q1) = 2 x 66.67
Q1 = 2x66.67/3 C = 44.45 C
and Q2 = 2 x 44.45 C = 88.9 C

Potential difference arcoss across each capacitor = 44.45/1 v = 44.45 v

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