Question

16. The given graph shows variation of charge 'q' versus potential difference 'V for two capacitors
C and C2. Both the capacitors have same plate separation but plate area of C2 is greater than
that of C. Which line (A or B) corresponds to C, and why?
​

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.

Calculate :

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

$\: \: \: ❍ \: \boxed{ \underline{ \rm\therefore \: q = C \times V∴q=C×V}}$

Comparing this with standard linear equation,

$\: \: \: \: \: \: ❍ \: \: \underline{\boxed{ \rm{y = mx + c}}}$

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

$\: \: \: \: \: \: \: \: \: \: \red❍ \space{\underline{ \rm\therefore \: q = C \times V∴q=C×V}}$

$\: \: \: \purple❂ \: \boxed{ \rm\: q = \bigg \{ \dfrac{\epsilon_{0}A}{D} \bigg \}}$

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

For Capacitor A :

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

For Capacitor B:

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

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