Question

The given graph shows the variation of charge q versus potential difference V for two capacitors C₁ and C₂. The two capacitors have the same plate separation but the plate area of C₂ is double than that of C₁. Which of the lines in the graph correspond to C₁ and C₂ and why?

Answer 1

Since capacitance of a capacitor is given by

C = \(\frac{\varepsilon_0A}{d}\) 

Here d is the same for both the capacitors.

So C ∝ A

As area of C₂ = 2 x Area of C₁

∴ C₂ = 2 C₁

Also C = \(\frac{q}{V}\). 

Thus the slope of q -V graph gives the value of capacitance. Here slope for A is greater than B, hence graph A corresponds to C₂ and graph B corresponds to C₁.