Introduction to Energy Stored in a Capacitor Equation
Capacitance:
Different conductors have different capacities to hold electric charge. The capacity of a conductor to hold charge depends upon the shape, size and surroundings of the conductor. The capacity of a conductor to hold charge is called capacitance.I like to share this paper capacitor with you all through my article.
For an isolated conductor when we increase the charge on the conductor, its potential also gets increased. The charge on the conductor is directly proportional to the potential of the conductor.
Q a V
Q = CV
Here C is proportionality constant called as capacitance. So capacitance is
C = Q / V
Unit of capacitance is coulomb / volt or farad.
Energy Stored in a Capacitor Equation:
Consider an uncharged capacitor of capacitance C. The capacitor is charged to a potential V when connected to a battery. Let the charge on the capacitor is Q. Suppose at any intermediate state of charging, let the instantaneous charge on the capacitor be q and potential difference across the capacitor is
dV = q /C. The work done to increase the charge dq is given as
dW = dV.dq
= (q /C) dq
The total work done to charge the capacitance from q = 0 to final charge
q = Q is i. e. is the energy stored in capacitor.
W = ? (q/C) dq
= (1/C) (Q2/2)
= Q2 /2C ……….. (1)
= (CV)2 /2C
U = (1/2)CV2 ……….. (2)
Equation (1) & (2) are the relation for energy stored in capacitor.
Effect of Dielectric on Energy Stored in a Capacitor on Equation:
1) When a charging battery is removed from the capacitor and dielectric of constant k is added, then the energy stored in the capacitor decreases by k times.
2) When a dielectric of constant k is added keeping the charging battery connected to the capacitor, then the energy stored in the capacitor increases by k times.
Capacitance:
Different conductors have different capacities to hold electric charge. The capacity of a conductor to hold charge depends upon the shape, size and surroundings of the conductor. The capacity of a conductor to hold charge is called capacitance.I like to share this paper capacitor with you all through my article.
For an isolated conductor when we increase the charge on the conductor, its potential also gets increased. The charge on the conductor is directly proportional to the potential of the conductor.
Q a V
Q = CV
Here C is proportionality constant called as capacitance. So capacitance is
C = Q / V
Unit of capacitance is coulomb / volt or farad.
Energy Stored in a Capacitor Equation:
Consider an uncharged capacitor of capacitance C. The capacitor is charged to a potential V when connected to a battery. Let the charge on the capacitor is Q. Suppose at any intermediate state of charging, let the instantaneous charge on the capacitor be q and potential difference across the capacitor is
dV = q /C. The work done to increase the charge dq is given as
dW = dV.dq
= (q /C) dq
The total work done to charge the capacitance from q = 0 to final charge
q = Q is i. e. is the energy stored in capacitor.
W = ? (q/C) dq
= (1/C) (Q2/2)
= Q2 /2C ……….. (1)
= (CV)2 /2C
U = (1/2)CV2 ……….. (2)
Equation (1) & (2) are the relation for energy stored in capacitor.
Effect of Dielectric on Energy Stored in a Capacitor on Equation:
1) When a charging battery is removed from the capacitor and dielectric of constant k is added, then the energy stored in the capacitor decreases by k times.
2) When a dielectric of constant k is added keeping the charging battery connected to the capacitor, then the energy stored in the capacitor increases by k times.