Question

Three capacitors of capacitance $3\mu \text{F},10\mu \text{F}$ and $15\mu \text{F}$ are connected in series to a battery of $100\text{V}$. The ratio of voltage across $10\mu \text{F}$ and $15\mu \text{F}$ is

• A. $2:3$
• B. $1:3$
• C. $1:2$
• D. $3:2$

Answer 1

The correct option is D $3:2$

Given:
$C_1=3\mu \text{F};C_2=10\mu \text{F};C_3=15\mu \text{F}$

As we know that, in a series combination, the charge on each capacitor is the same, which is the same as the charge on the equivalent capacitor.

From formula, $Q=CV$,
Since, here $Q$ is constant,

$\therefore V\propto \frac{1}{C}$

$\Rightarrow \frac{V_2}{V_3}=\frac{C_3}{C_2}=\frac{15}{10}$

So, $\frac{V_2}{V_3}=\frac{3}{2}$

Therefore, option $\left(d\right)$ is correct.