Question

Three capacitors are connected as shown in the figure, where $C_1=3\mu F,C_2=6\mu F,C_3=2\mu F$ and $E=10\text{Volt}$.
Which of the following statements is/are true ?
(1) energy drawn from the source is $2\times {10}^{–4}\text{J}$.
(2) energy drawn from the source is $4\times {10}^{–4}\text{J}$.
(3) heat generated in the system during charging is $2\times {10}^{–4}\text{J}$.
(4) charges on the three capacitors are equal.

• A. 1 and 3
• B. 2 and 3
• C. 1, 3 and 4
• D. 1 only

Answer 1

The correct option is C 1, 3 and 4

$C_{1eq}=\frac{6\times 3}{6+3}=2\mu F$
$C_{2eq}=2\mu F$
$C_{eq}$ for the given circuit is
$C_{eq}=\left(\frac{3\times 6}{6+3}\right)+2=2+2$
$C_{eq}=4\mu F$
Now, we know that
$Q=C_{eq}.V$
$Q=4\times {10}^{-6}\times 10$
$\Rightarrow Q=40\mu C$

Energy drawn from the source $=\frac{1}{2}{C}_{eq}{V}^2$
$=\frac{1}{2}\times 4\times {10}^{-6}\times 100$
$=2\times {10}^{-4}\text{J}$

Heat generated = W.D. = Energy
$\Rightarrow$ Heat generated $=2\times {10}^{-4}\text{J}$
Since, capacitance of branch (1) and (2) are same also potential across branch (1) and (2) are same as they are connected in parallel to source.
$\Rightarrow Q_1=Q_2$
Also as $3\mu F$ and $6\mu F$ capacitor are connected in series so, same charge will flow through them
$\Rightarrow$ charge on three capacitors are equal.
$\therefore$ (C) 1,3 and 4