Question

An air capacitor of capacity $10\mu \text{F}$ is connected to a battery of $12\text{V}$. Now the space between the plates is filled with a liquid of dielectric constant $5$. The additional charge that flows to the capacitor is

• A. $120\mu \text{C}$
• B. $600\mu \text{C}$
• C. $480\mu \text{C}$
• D. $24\mu \text{C}$

Answer 1

The correct option is C $480\mu \text{C}$

Before the dielectric is inserted, charge on capacitor,

$Q=CV=10\times 12=120\mu \text{C}$

After the dielectric is inserted with battery connected, new charge,

$Q^{\prime }=KCV=5\times 120=600\mu \text{C}$

The additional charge that flows to the capacitor is given by

$Q^{\prime }-Q=600-120=480\mu \text{C}$

Hence, option $\left(c\right)$ is correct.

Key concept: The capacitance increases by a factor $K$ with the introduction of a dielectric material completely occupying the space between the plates.