Three capacitors, having capacitances \(C_1=2~\text{pF},~C_2=3~\text{pF},~\text{and}~C_3=4~\text{pF}\) are connected in parallel and then connected to a \(100~\text V\) supply. What is the total capacitance of this combination, and what are the charges \(Q_1,\) \(Q_2,\) and \(Q_3\) on capacitors \(C_1,~C_2\) and \(C_3\) respectively?
| 1. | \(C_{total}=9~\text{pF};~Q_1=200~\text{pC},~Q_2=300~\text{pC},~Q_3=400~\text{pC}\) |
| 2. | \(C_{total}=4~\text{pF};~Q_1=400~\text{pC},~Q_2=300~\text{pC},~Q_3=200~\text{pC}\) |
| 3. | \(C_{total}=9~\text{pF};~Q_1=400~\text{pC},~Q_2=300~\text{pC},~Q_3=200~\text{pC}\) |
| 4. | \(C_{total}=2~\text{pF};~Q_1=200~\text{pC},~Q_2=400~\text{pC},~Q_3=300~\text{pC}\) |
(1) Given, C1 = 2pF, C2 = 3pF and C3 = 4pF.
Equivalent capacitance for the parallel combination is given by Ceq .
Therefore, Ceq = C1 + C2 + C3 = 2 + 3 + 4 = 9pF
Hence, total capacitance of the combination is 9pF.
(2) supply voltage, V = 100v
The three capacitors are having the same voltage, V = 100v
q = vc
where,
q = charge
c = capacitance of the capacitor
v = potential difference
for capacitance, c = 2pF
q = 100 x 2 = 200pC = 2 x 10-10C
for capacitance, c = 3pF
q = 100 x 3 = 300pC = 3 x 10-10C
for capacitance, c = 4pF
q = 100 x 4 = 400pC = 4 x 10-10 C
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