Question 511: Electrostatics & Capacitance

Question

In a parallel plate capacitor with air between the plates, the distance $$d$$ between the plates is changed and the space is filled with dielectric constant 8. The capacity of the capacitor is increased 16 times, the distance between the plates is

Accepted Answer

Capacitance of a parallel plate capacitor is given by, $$C=\frac{\varepsilon_0 A}{d}$$
When capacitor is completely filled with dielectric $$K$$ then, $$C^{\prime}=\frac{\varepsilon_0 K A}{d^{\prime}}$$
According to question, $$\frac{C^{\prime}}{C}=\frac{16}{1}=\frac{\frac{\varepsilon_0 	imes 8 	imes A}{d^{\prime}}}{\frac{\varepsilon_0 	imes A}{d}}$$
$$\begin{aligned}
\Rightarrow & \quad \frac{16}{1} =\frac{8 d}{d^{\prime}} \
\Rightarrow & \quad d^{\prime} =\frac{d}{2}
\end{aligned}$$

Answer

2d

Answer

4d

Answer

d/2

Answer

d/4

Electrostatics & Capacitance

In a parallel plate capacitor with air between the plates, the distance $d$ between the plates is changed and the space is filled with dielectric constant 8. The capacity of the capacitor is increased 16 times, the distance between the plates is

Choose the correct answer: