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  4. A voltmeter reads 4 V when connected to a parallel plate capacitor with air as a dielectric. When a dielectric slab is introduced between plates for the same configuration voltmeter reads 2 V. What is the dielectric constant of the material ?

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Q. A voltmeter reads $4\, V$ when connected to a parallel plate capacitor with air as a dielectric. When a dielectric slab is introduced between plates for the same configuration voltmeter reads $2\, V$. What is the dielectric constant of the material ?

KCETKCET 2014Electrostatic Potential and Capacitance

Solution:

Given, $V_{0}=4\, V ,\, V_{1}=2\, V ,\, K$ = ?
By dielectric constant $K=\frac{C}{C_{0}}$
where $C_{0}$ is the capacitance when the space between the two plates of the capacitor is an air and $C$ is the capacitance when the space is filled with dielectric material.
As we know that $q=CV$
i.e., $C \propto \frac{1}{V}$
So, $K=\frac{4}{2}=2$