Question

Suppose the two plates of a capacitor have different areas. When the capacitor is charged by connecting it to a battery, do the charges on the two plates have equal magnitude, or may they be different? Explain your reasoning.

Short answer

The presence of free charges in abundance causes the capacitance to increase. So, the charge stored is different.

Step-by-step solution

Concept of capacitance.

Capacitance is the measure or the capacity of an electric device to store charge and allow the device to use the charge up as desired. The difference in potential causes the charge to get stored on the plates of conductor.

Mathematically,

$\mathbf{C}\mathbf{=}\frac{\mathbf{Q}}{\mathbf{V}}$......(1)

Where, Q is the total charge stored and V is the potential difference or the voltage applied electronically.

Explanation of the argument.

The expression of capacitance in terms of area and inter-plate distance is,

$C=\frac{{\epsilon }_{0}A}{d}$

So, it is clear that the capacitance is directly proportional to the area of the plates that carries the charges, or lets the charges stay. Therefore, as area increases capacitance also increases.

Rearrange equation (i),

$Q=CV$

So, the charge stored is directly linked to the capacitance. Therefore, it can be concluded that the plates with larger surface area charges more, or holds more charge.