# 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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