In: Physics

# 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.

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?

## Solutions

##### Expert Solution

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,

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