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Question
Deduce an expression for equivalent capacitance C when three capacitors C1, C2 and C3 connected in parallel.
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Solution
An expression for effective capacitance in the parallel grouping of capacitors :
Consider three capacitors of capacitance C1 , C2 and C3 are connected in parallel.
Let Q1, Q2 and Q3 be the charges deposited on the capacitors as shown in the figure.
Suppose a potential difference ‘V ’ is applied across the combination. Then, the potential difference between the plates of each capacitor is V but charges on each capacitor are different. Since different current flows through different branches, so the charges are given by
`Q_1 = C_1V.Q_2 = C_2V. Q_3 = C_3V` ....(i)
From the principle of conservation of charge
`Q = Q_1 + Q_2 + Q_3`
`Q = C_1V + C_2V + C_3V` [From equation (i)]
`∴ Q = V(C_1 + C_2 + C_3)`
If these capacitors are replaced by a single capacitor of capacity CP such that `Q = C_PV` then using equation (ii) we have,
`C_PV = V(C_1+C_2+C_3)`
`C_P = C_1+C_2+C_3`
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