Question

A battery does 200 J of work in charging a capacitor. The energy stored in the capacitor is?
(a). 200J
(b). 100J
(c). 50J
(d). 400J

Answer 1

- Hint- In order to find the energy stored in the capacitor we will use the basic concept of physics which states that when a capacitor charges by a battery, the energy that is stored will be equal to the half of the work done by the battery.

Formula used- \[W = QV,E = \dfrac{1}{2}\left( {QV} \right)\]

Complete step-by-step solution -

Given that
Work done by a battery in charging a capacitor, W = 200 Joules
We have to find the energy stored in the capacitor.
As we know that when a capacitor charges by a battery, the energy that is stored will be equal to the half of the work done by the battery.
Work done by the battery is \[W = QV\] ---- (1)
Where Q is the charge and V is the potential difference.
Energy stored in a capacitor is, \[E = \dfrac{1}{2}\left( {QV} \right)\]
Substitute the value of W from equation (1), we have
\[
  \because E = \dfrac{1}{2}\left( {QV} \right) \\
   \Rightarrow E = \dfrac{1}{2}\left( W \right){\text{ }}\left[ {\because W = QV} \right] \\
   \Rightarrow E = \dfrac{1}{2}\left( {200J} \right){\text{ }}\left[ {\because W = 200J} \right] \\
   \Rightarrow E = 100J \\
 \]
Hence, energy stored in the capacitor is 100 Joules
So, the correct answer is option B.

Note- Work is closely related to energy. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Energy is the capacity or power to do work, such as the capacity to move an object (of a given mass) by the application of force.