Question 307: Electrostatics & Capacitance

Question

Two capacitors of capacitances C and 2C are
charged to potential differences V and 2V,
respectively. These are then connected in
parallel in such a manner that the positive
terminal of one is connected to the negative
terminal of the other. The final energy of this
configuration is :

Accepted Answer

By conservation of charge,
$${q_1} + {q_2} = {q_1}' + {q_2}'$$
$$ \Rightarrow $$ $$ - CV + (2C)(2V) = (C + 2C)V'$$
$$V' = {{3CV} \over {3C}} = V$$
$${U_f} = {1 \over 2}C{v^2} + {1 \over 2}(2C){V^2}$$
$${U_f} = {3 \over 2}C{V^2}$$

Answer

Zero

Answer

$${3 \over 2}C{V^2}$$

Answer

$${9 \over 2}C{V^2}$$

Answer

$${{25} \over 6}C{V^2}$$

Electrostatics & Capacitance

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is :

Choose the correct answer: