A $ 400\,pF $ capacitor is charged by a $ 100\,V $ supply. How much electrostatic energy is lost in the process of disconnecting from the supply and connecting another uncharged $ 400\,pF $ capacitor?
$C=400 \times 10^{-12} F$ $V=100\, V$ Initially energy stored $=\frac{1}{2} C V^{2}$ $=\frac{1}{2} 400 \times 10^{-12} \times\left(10^{2}\right)^{2}$ $=\frac{1}{2} \times 4 \times 10^{-10} \times 10^{4}$ $=2 \times 10^{-6} J$ $\Rightarrow Q=C V=4 \times 10^{-10} \times 100$ $=4 \times 10^{-8} C$ $\Rightarrow$ By again connecting the charged capacitor with a uncharged ideal capacitor. $\Rightarrow$ Now, the charge $Q$ will divide into two capacitors. $\Rightarrow$ As $V$ and $C$ are same for both, $Q'$ will be same for both, $\Rightarrow$ So $Q'=\frac{Q}{2}=2 \times 10^{-8} C$ $\Rightarrow$ So, energy stored in both the capacitors $=\left(\frac{\left(Q'\right)^{2}}{2 C}\right)=\frac{\left(Q'\right)^{2}}{2 C}$ $=\frac{\left(2 \times 10^{-8}\right)}{8 \times 10^{-10}}=10^{-6} J$ So energy lost $=2 \times 10^{-6}-0.25 \times 10^{-6}$ $=0.75 \times 10^{-6} J \approx 10^{-6} J$
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Top Questions on electrostatic potential and capacitance
The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.
Some major things that we should know about electric potential:
They are denoted by V and are a scalar quantity.
It is measured in volts.
Capacitance
The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.
The capacitor is in Series and in Parallel as defined below;
In Series
Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitor’s capacitance.
In Parallel
Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitor’s capacitance.
