Question

A condenser charged to a potential of 300 volts has an energy of one joule. What is its capacitance?

Answer 1

Hint: As we are asked to find the value of the capacitance of the charged condenser, so, we will make use of the formula that is used to find the energy stored in the capacitor. The capacitance of the conductor is the product of 2 times the energy stored and the square of the potential supplied.

Formula used: \[U=\dfrac{1}{2}C{{V}^{2}}\]

Complete step by step answer:
The formula that relates the energy stored in a charged condenser, the potential difference and the capacitance is given as follows.
\[U=\dfrac{1}{2}C{{V}^{2}}\]
Where \[U\] is the energy stored in the condenser, \[C\] is the capacitance of the condenser and \[V\] is the potential difference applied to the condenser.
From the data, we have the data as follows.
The energy stored in the charged condenser is, U = 1 J
The potential applied across the charged condenser is, V = 300 volt
Substitute the given values in the above formula to find the value of the capacitance of the conductor.
Upon substituting these values, we get the value of the capacitance as follows.
\[\begin{align}
  & 1=\dfrac{1}{2}\times C\times {{300}^{2}} \\
 & \Rightarrow C=\dfrac{2}{{{300}^{2}}} \\
\end{align}\]
Upon further calculating, we get the value of the capacitance of the conductor as,
\[C=6.66\times {{10}^{-5}}\,F\]

Therefore, the value of the capacitance of the charged conductor having the energy to be 1 J and supplied with the potential of 300 V is \[6.66\times {{10}^{-5}}\,F\].

Note: In this case, we are asked to find the value of the capacitance of the charged condenser. Even, they may further ask to find the value of the charge stored, in such case, we need to multiply the capacitance of the charged condenser by the voltage supplied across the condenser. Even the units of the parameters should be taken care of.