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Charge in the each capacitor when connected in parallel

Physics Asked on March 12, 2021

Consider a situation where we have three capacitors of capacitances A, B and C connected in parallel to a battery of emf V. The equivalent capacitance of the combination would be A + B + C. The charge in the equivalent capacitor would therefore be V times A+B+C. Let’s call it Q.
Is Q the sum of charges on all the three capacitors A, B and C or the charge in each capacitor?

2 Answers

It is the sum of charge on all 3 capacitors. This is because the charge on a single ideal capacitor only depends on the voltage applied across it. When wired in parallel, each capacitor gets the same voltage. The charge on one of them is then independent of the others being present, so the total charge is $Q=V (A+B+C)$.

Answered by noah on March 12, 2021

Capacitors in parallel have the same voltage, since you know the following relation

$$Q=CV$$

One can write down $Q_{total}$ based on our initial statement aka $V_{total}=V$ where $V$ is the voltage through each capacitor

$$Q_{total} = C_{total}V_{total}= C_A V+C_B V+C_C V = V( C_A +C_B +C_C) $$

Where $C_i$ stands for different capacitance $i=A, B, C$. After simplifying the voltages you get the parallel capacitance relation as

$$C_{total}= C_A +C_B +C_C $$

For the total charge, check the equation before the last one

Answered by Monopole on March 12, 2021

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