Three Identical Capacitors C1 C2 And C3 Of Capacitance 6μf Each Are Connected To A 12 V Battery. Find The Charge On Each Capacitor.

As given in the question:Three identical capacitor\( C_{1} C_{2} , C_{3} \) of capacitance 6μF each are connected to a 12V Battery as shown below.

Capacitor \( C_{1} \) and Capacitor \( C_{2} \)are in series having potential difference of 12V at \( C_{3} \).

Therefore, an effective capacitance of \(C_{1} \)and \(C_{2}\) is

\( C_{12} = \frac{C_{1} * C_{2}}{C_{1} + C_{2}}\) \( \Rightarrow \frac{6 * 6}{6 + 6}\) \( \Rightarrow 2 \mu F\)

Charge on each of capacitors \( C_{1} \) and Capacitor \( C_{2}\) is same as being in series

\( q_{1} = q_{2} = C_{12} V = (3μF) (12 V) = 36μC\) \( Charge of C_{3} , q_{3} = C_{3}V\)

=\( (6μ F * 12V) = 72μC\)

Therefore, the charge on each capacitor will be:

\( C_{1} = 36μC.\) \( C_{2} = 36μC.\) \( C_{3} = 72μC.\)

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