A circular parallel plate capacitor with radius 6cm is separated by 0.12cm. Calculate the capacitance of the…

1. Analyze the question

We are asked to calculate the capacitance ($C$) of a parallel plate capacitor. We are given:

• Radius of the plates ($r$) = 6 cm = 0.06 m
• Separation distance ($d$) = 0.12 cm = 0.0012 m
• Permittivity of free space ($\varepsilon_0$) = $8.85 \times 10^{-12} \, \text{F/m}$
• $\pi = 3.142$

2. Explain the concept

The capacitance of a parallel plate capacitor is given by the formula:

Where:

• $A$ is the area of the plates. Since the plates are circular, $A = \pi r^2$.
• $d$ is the distance between the plates.
• $\varepsilon_0$ is the permittivity of free space.

3. Show the solution

Step 1: Calculate the area ($A$)

Step 2: Calculate the capacitance ($C$) Substitute the values into the formula $C = \frac{\varepsilon_0 A}{d}$:

First, multiply the numerator:

Now, divide by the distance ($d = 1.2 \times 10^{-3}$):

To express this in the format of the options (using $10^{-11}$):

4. Identify the answer

Comparing our result to the given options, $8.34 \times 10^{-11} \, \text{F}$ matches option C.

5. Tip

Always convert your units to SI units (meters) before plugging them into the formula. A common mistake in JAMB Physics is forgetting to convert centimeters to meters, which will lead to a massive error in your final answer. Remember: $1 \, \text{cm} = 10^{-2} \, \text{m}$.