Question

a capacitor stores energy u1 when it holds charge Q .The same capacitor stores energy u2 when it holds charge 16 Q what is the ratio between u2/u1 the answer is 256 why ?

Answer 1

Answer:

Ratio between U₂/U₁ = 256

Explanation:

Energy stored in a capacitor is given by

      $U=\frac{1}{2}\frac{Q^2}{C}$

where Q is the charge and C is the capacitance.

We have

     $U_1=\frac{1}{2}\frac{Q^2}{C}$

and

     $U_2=\frac{1}{2}\frac{(16Q)^2}{C}=\frac{1}{2}\frac{256Q^2}{C}$

So,

     $\frac{U_2}{U_1}=\frac{\frac{1}{2}\frac{256Q^2}{C}}{\frac{1}{2}\frac{Q^2}{C}}=256$

Ratio between U₂/U₁ = 256