Question

A capacitor of capacitance C is charged to potential V and another capacitor of capacitance 2C is charged to potential 2V.Then they are joined across each other with plates of same polarity together.The amount of heat generated after connecting the two capacitors together is​

Answer 1

Answer:

Explanation:

Common potential v equal total chargeupon total capacitance i. E. V =(c1v1 +c2v2) / c1+c2

Answer 2

Answer:

The amount of heat generated after connecting the two capacitors together is​ $\frac{25}{6} J$.

Explanation:

When the plates of the same polarity are connected together then common potential is given as,

$V=\frac{C_1V_1+C_2V_2}{C_1+C_2}$        (1)

Where,

V=common potential

C₁=capacity of the first capacitor

V₁=potential across the first capacitor

C₂=capacity of the second capacitor

V₂=potential of the second capacitor

From the question we have,

C₁=C

V₁=V

C₂=2C

V₂=2V

By substituting the required values in equation (1) we get;

$V'=\frac{C\times V+2C\times2V}{C+2C}=\frac{5CV}{3C}=\frac{5}{3} V$       (2)

The amount of heat generated after connecting the two capacitors together is,

$U=\frac{1}{2} C'V^2$                (3)

Here in equation (3) C'  will be equivalent capacitance. Which is given as,

$C'=C+2C=3C$       (4)

By substituting equations (2) and (4) in equation (3) we get;

$U=\frac{1}{2} \times 3C\times (\frac{5}{3}V )^2$

$U=\frac{25}{6} J$

Hence, the amount of heat generated after connecting the two capacitors together is​ $\frac{25}{6} J$.