Question

A \[2\mu f\]capacitor is charged to 100 V, and then its plates are connected by a conducting wire. The heat produced is:
A) \[0.001J\]
B) \[0.01J\]
C) \[0.1J\]
D) \[1J\]

Answer 1

Hint:In this question, we are going to use the concept of energy stored in the capacitor as heat is also a form of energy so its value can be calculated through the expression of energy stored in the capacitor.
Formula used:
Energy stored in capacitor, \[E = \dfrac{1}{2}C{V^2}\]
Here, $C$ is capacitance of the capacitor
$V$ is the voltage applied across the capacitor

Complete step by step answer:
It is given in the question that
$C = 2\mu f = 2 \times {10^{ - 6}}f$
$V = 100V$
Substitute the given values in the formula to get
The total amount of energy stored in capacitor, \[E = \dfrac{1}{2}C{V^2}\]
\[ = \dfrac{1}{2} \times 2 \times {10^{ - 6}} \times {100^2}\]
\[ = {10^{ - 6}} \times {10^4}\] $\left( {\because {{100}^2} = 10000 = {{10}^4}} \right)$
\[ = {10^{ - 6 + 4}}\] $\left( {\because {a^m}{a^n} = {a^{m + n}}} \right)$
\[ = {10^{ - 2}}\]
$ = \dfrac{1}{{100}}J$
$ \Rightarrow E = 0.01J$
So, after connecting both the plates, total energy will convert into heat.
So, amount of heat produced\[ = 0.01J.\]
Therefore, the correct answer is (B) \[ = 0.01J.\]
Additional Information:
Capacitor: The capacitor is a component which has the ability or “capacity” to store energy in the form of an electrical charge producing a potential difference across its plates.
Different types of capacitors:
1. Electrolyte capacitor
2. Mica capacitor
3. Paper capacitor
4. Film capacitor
5. Non-polarized capacitor
6. Ceramic capacitor
Capacitors are formed by charging one plate and connecting the second plate to the ground. Due to which a potential difference is created between the two plates which results in the stored charge.

Note:We have used the law of conservation of energy to solve this problem. It states that energy can neither be created nor be destroyed. It can only be transformed from one type to another. Using this law, we concluded that the energy stored in the capacitor will be the heat energy.