Question

The given graph shows that variation of charge q versus potential difference V for two capacitors A and B. The two capacitors have same plate separation but the plate area of B is double than that of A. Which of the lines in the graph correspond to A and B ? Justify.

Answer 1

Given:

The two capacitors have same plate separation but the plate area of B is double than that of A.

To find:

q - V graph for the capacitors.

Calculation:

The relationship between charge and potential difference at steady state of capacitor :

$\therefore \: q = C \times V$

Comparing this with standard linear equation,

$\boxed{ \sf{y = mx + c}}$

We can say that it will be a linear graph in the first quadrant passing through the origin without intercept.

$\therefore \: q = C \times V$

$= > \: q = \bigg \{ \dfrac{\epsilon_{0}A}{D} \bigg \} \times V$

So the slope of the graph will depend on the dimensions of the capacitors ;

For Capacitor A :

$\boxed{ \sf{\: q = \bigg \{ \dfrac{\epsilon_{0}A}{D} \bigg \} \times V}}$

For Capacitor B:

$\boxed{ \sf{\: q = \bigg \{ \dfrac{\epsilon_{0}(2A)}{D} \bigg \} \times V}}$

Hence the slope of the graph of B will be higher than graph A .

Refer to the attached diagram.