Question

A 1.2 nF parallel-plate capacitor has an air gap between its plates. Its capacitance increases by 3.0 nF when the gap is filled by dielectric. What is the dielectric constant of that dielectric?

Answer 1

The capacitance of the capacitor when the gap

between the plates filled with dielectric is

$$ \begin{aligned} C &=C_{0}+3.0 \mathrm{nF} \\ &=1.2 \mathrm{nF}+3.0 \mathrm{nF} \\ &=4.2 \mathrm{nF} \end{aligned} $$

the capacitance of the parallel plate capacitor

without dielectric is

$$ C_{0}=\frac{\varepsilon_{0} A}{d} $$

the capacitance of the parallel plate capacitor

with dielectric is

$$ C=\frac{K \varepsilon_{0} A}{d} $$

Hence, the dielectric constant of that dielectric is,

$$ K=\frac{C}{C_{0}}=\frac{4.2 \mathrm{nF}}{1.2 \mathrm{nF}}=3.5 $$