Question

A capacitor is connected to a $10\text{V}$ battery. When the medium is air, the charge on plates is $40\mu \text{C}$ . When the medium between plates is oil, the charge on plates becomes $100\mu \text{C}$ . The dielectric constant of oil is

• A. $2.5$
• B. $4$
• C. $6.25$
• D. $10$

Answer 1

The correct option is A $2.5$

Given that,
Potential difference of battery, $V=10\text{V}$

Before the oil is inserted, charge on capacitor is given by

$Q=CV=40\mu \text{C}$

Let the dielectric constant of oil is $K$, then new charge given by

$Q^{\prime }=KCV=100\mu \text{C}$

Now, $\frac{Q^{\prime }}{Q}=\frac{KCV}{CV}=\frac{100}{40}$

$\Rightarrow K=2.5$

Hence, option (a) is the correct answer.