Question

An air filled 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. $240\mu \text{C}$

Answer 1

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

Before the dielectric is inserted, charge on capacitor is given by $$Q=CV$$$\Rightarrow Q=10\times 12=120\mu \text{C}$

After the dielectric is inserted with battery connected, new charge, $$Q^{\prime }=KCV$$$\Rightarrow Q^{\prime }=5\times 120=600\mu \text{C}$

The additional charge that flows to the capacitor
$=Q^{\prime }-Q$
$=600-120$
$=480\mu \text{C}$

Hence, option (c) is the correct answer.

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