Question

A capacitor of $12\mu$ capacitance can be fully charged after it is connected between a potential difference of $9\;V$. How much electrical energy is used in charging the capacitor?
\[\begin{align}
  & A.4.86\times {{10}^{-4}}J \\
 & B.54\times {{10}^{-4}}J \\
 & C.1.0\times {{10}^{-4}}J \\
 & D.9.72\times {{10}^{-4}}J \\
\end{align}\]

Answer 1

Hint: We know that the energy of the capacitor is $E=\dfrac{1}{2}CV^{2}$. Since here, we have a fully charged capacitance which is attached to some potential, it will also release some charge, which in turn will also contribute to the energy.

Formula used: $E=\dfrac{1}{2}CV^{2}$.

Complete step by step answer:
A capacitor is a two terminal component that stores electrical energy in the form of potential energy, and later discharges them. This property is called the capacitance of the capacitor.
Given that, a fully charged capacitance of $C=12\mu F$ is connected to $V=9V$. Then the charge $Q$ produced is given as $Q=CV$.
Then we have, $Q=12\times 10^{-6}\times 9= 108 \times 10^{-6}= 108\mu C$
We know that the energy of the capacitor is $E=\dfrac{1}{2}CV^{2}$ ,where $C$ is the capacitor and $V$ is the potential difference. We can also say that $E=\dfrac{Q^{2}}{2C}$.
Then, we have, $E=\dfrac{(108\times 10^{-6})^{2}}{2\times 12\times 10^{-6}}$
$\implies E=486\times 10^{-6}J=4.86\times 10^{-4}J$

So, the correct answer is “Option A”.

Additional Information: A capacitor can store electrical energy, and behaves as a temporary battery. They are used mainly to maintain the power supply while batteries are being changed. It can also store information in the form of binary digits. It is the main component used in full wave and half wave rectifiers. (symbol: F), named after the English physicist Michael Faraday. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates. The series of capacitors is the sum of reciprocal of its individual capacitors, whereas in resistance the parallel is the sum of reciprocal of its individual resistors. Also remember that capacitors can charge and discharge.

Note: The series of capacitors is the sum of reciprocal of its individual capacitors, whereas in resistance the parallel is the sum of reciprocal of its individual resistors. Also remember that capacitors can charge and discharge.