Question

A $1\mu F$ and a $2\mu F$ capacitor are connected in series across a $1200V$ supply. The charged capacitors are disconnected from the line and from each other and are now reconnected with the terminals of like sign together. Find the final charge on each capacitor and the 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 potential difference across each capacitor is $800V$.
• D. Charge and potential difference across each capacitor are zero.

Answer 1

The correct option is B Charges on capacitors are $1600/3\mu C$ and $3200/3\mu C$, and the potential difference across each capacitor is $1600/3V$

$1200-\frac{q}{1}-\frac{q}{2}=0orq=800\mu C$
Charge on each capacitor is $800\mu C$.
$V_1=\frac{q}{C_1}=\frac{800}{1}=800V$
$V_2=\frac{q}{C_2}=\frac{800}{2}=400V$
$q_1^{\prime }+q_2^{\prime }=1600.......\left(i\right)$
Also $\frac{q_1^{\prime }}{1}-\frac{q_2^{\prime }}{2}=0$
or $q_2^{\prime }=2q_1^{\prime }$
From Eq (i), $3q_1^{\prime }=1600or{q}_1^{\prime }=\frac{1600}{3}\mu C$
$3q_2^{\prime }=\frac{3200}{3}\mu C$
$V=\frac{q_1+q_2}{C_1+C_2}=\frac{1600}{3}V$