Question

A $1\mu F$ and a $2\mu F$ capacitor are connected in series across a $1200V$ supply. If the charged capacitors are reconnected with the terminals of opposite signs together, find the final charge and voltage across each capacitor.

• A. Charges on capacitors are $1400/3\mu C$ and $3200/3\mu C$, and the potential difference across each capacitor is $1600/3V$
• B. Charges on capacitors are $1600/3\mu C$ and $3200/3\mu C$, and the potential difference across each capacitor is $1600/3V$
• C. Charge on each capacitor is $1600\mu C$, and the potential difference across each capacitor is $800V$.
• D. Charge and potential difference across each capacitor are zero.

Answer 1

The correct option is D Charge and potential difference across each capacitor are zero.

$1200-\frac{q}{1}-\frac{q}{2}=0orq=800\mu C$

Charge on each capacitor is $800\mu C$.

$V_1=\frac{q}{C_1}=\frac{800}{1}=800V$

$V_2=\frac{q}{C_2}=\frac{800}{2}=400V$

$q_1^{\prime }+q_2^{\prime }=800-800=0.........\left(ii\right)$

Also, $\frac{q_1^{\prime }}{1}-\frac{q_2^{\prime }}{2}=0$

From Eq (ii), $q_1^{\prime }=q_2^{\prime }=0$

Therefore, potential difference across each capacitor is zero.