A 600pF capacitor is charged by a 200V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
Solution and Explanation
Capacitance of the capacitor, C = 600 pF
Potential difference, V = 200 V
Electrostatic energy stored in the capacitor is given by,
\(E1=\frac{1}{2} CV^2=\frac{1}{2}X(600×10^-12)×(200)^2 J=1.2×10^{-5}J\)
If supply is disconnected from the capacitor and another capacitor of capacitance C = 600 pF is connected to it, then equivalent capacitance (Ceq) of the combination is given by,
\(\frac{1}{C_eq}=\frac{1}{C}+\frac{1}{C}\)
\(\frac{1}{Ceq} =\frac{1}{600}+\frac{1}{600} = \frac{2}{600}=\frac{1}{300 }= 300 pF\)
New electrostatic energy can be calculated as
\(E2=1/2Ceq V2= \frac{1}{2}×300×(200)^2 J = 0.6 × 10-5 ^J \)
Loss in electrostatic energy = E1 – E2
= 1.2 × 10−5 0.6 × 10-5 J = 0.6 × 10-5 J = 6 × 10-6 J
Therefore, the electrostatic energy lost in the process is 6 × 10-6 J .
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Concepts Used:
Electrostatic Potential and Capacitance
Electrostatic Potential
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”.
Read More: Electrostatic Potential and Capacitance
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.