Question

In an RC-circuit, a resistance of R=1.0 "Giga Ohms" is connected to an air-filled circular-parallel-plate capacitor of diameter 12.0 mm with a separation distance of 1.0 mm. What is the time constant of the system?

Answer 1

Answer:

$\tau = 1\ ms$

Explanation:

First we need to find the capacitance of the capacitor.

The capacitance is given by:

$C = \epsilon_0 * area / distance$

Where $\epsilon_0$ is the air permittivity, which is approximately 8.85 * 10^(-12)

The radius is 12/2 = 6 mm = 0.006 m, so the area of the capacitor is:

$Area = \pi * radius^{2}\\Area = \pi * 0.006^2\\Area = 113.1 * 10^{-6}\ m^2$

So the capacitance is:

$C = \frac{8.85 * 10^{-12} * 113.1 * 10^{-6}}{0.001}$

$C = 10^{-12}\ F = 1\ pF$

The time constant of a rc-circuit is given by:

$\tau = RC$

So we have that:

$\tau = 10^{9} * 10^{-12} = 10^{-3}\ s = 1\ ms$