Question

What amount of heat will be generated in the circuit when switch S is shifted from position 1 to 2 in Figure ?

• A. $\frac{1}{2}C{V}_1^2$
• B. $\frac{1}{2}C{V}_2^2$
• C. $\frac{1}{2}C(V_1^2-V_2^2)$
• D. $\frac{1}{2}C(V_1-V_2{)}^2$

Answer 1

The correct option is B $\frac{1}{2}C{V}_2^2$

When switch is at position 1, charge on capacitor is $q_1=C(V_1-V_2)$
When switch is at position 2, charge on capacitor is $q_2=C{V}_1$
Now charge through $V_1$ cell is $\Delta q=q_2-q_1=C{V}_2$
By energy conservation, $U_2-U_1+$ Heat energy $=\Delta q{V}_1$
Heat energy $=C{V}_1{V}_2-\frac{1}{2}C{V}_1^2+\frac{1}{2}C(V_1-V_2{)}^2=C{V}_1{V}_2-\frac{1}{2}C{V}_1^2+\frac{1}{2}C{V}_1^2-2C{V}_1{V}_2+\frac{1}{2}C{V}_2^2=\frac{1}{2}C{V}_2^2$