Question

A1 $\mu F$ capacitor and a $2\mu F$ capacitor are connected in series across a $1200V$ supply line. The charged capacitors are disconnected from the line and from each other and reconnected with terminals of like sign together. Find the final charge on each and the voltage across them :

• A. $\frac{1600}{13}V$
• B. $\frac{1600}{32}V$
• C. $\frac{1600}{3}V$
• D. $\frac{160}{3}V$

Answer 1

Answer: (C)

$\frac{1600}{3}V$

$C_{net}=\frac{C_1{C}_2}{C_1+C_2}=\frac{2}{3}\mu F$

$q_{net}=C_{net}V$

$=\left(\frac{2}{3}\mu F\right)\left(1200V\right)$

$=800\mu C$

Now total charge will become $1600\mu C$. This will now distribute in direct ratio of capacity.

$\therefore \frac{q_1}{q_2}=\frac{C_1}{C_2}=\frac{1}{2}$

$q_1=\left(\frac{1}{3}\right)\left(1600\right)=\frac{1600}{3}\mu C$

$q_2=\left(\frac{2}{3}\right)\left(1600\right)=\left(\frac{3200}{3}\right)\mu C$

They will have a common potential (in parallel) given by;

$V=\frac{\text{Q}}{\text{C}}$

$=\frac{1600\mu C}{3\mu F}$

$=\frac{1600}{3}V$