A capacitor stores an energy of 8 Joules when there is a voltage of 51 volts across its terminals. A second identical capacitor of the same value is stores an energy of 2 Joules. What is the voltage across the terminals of the second capacitor?

6.38 V

Explanation:

Note: Since the capacitors are identical, The same Charge flows through them.

For the first capacitor,

The Energy stored in a capacitor is given as

E = 1/2qv ... Equation 1

Where E = Energy stored by the capacitor, q = charge in the capacitor v = Voltage.

make q the subject of the equation

q = 2E/v ... Equation 2

Given: E = 8 J, v = 51 v.

Substitute into equation 2

q = 8/51

q = 0.3137 C.

For the second capacitor,

v = 2E/q ... Equation 3

Given: q = 0.3137 C, E = 2 J.

Substitute into equation 3

v = 2/0.3137

v = 6.38 V

Hence the voltage across the second capacitor = 6.38 V