Derive an expression for the energy stored in a capacitor. Show that whenever two conductor share charges by bringing them into electrical contact, there is a loss of energy?
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Energy stored in a capacitor:
Capacitor is a charge storage device. Work has to be done to store the charges in a capacitor. This work done is stored as electrostatic potential energy in a capacitor.
Let q be the charge and V be the potential difference between the plates of the capacitor.If dq is the additional charge given to the plate, then work done is dw=Vdq
dw= q dq/ C. (since V=q/C)
Total work done to charge a capacitor is given by integrating dw
w= ½q²/C
This work done is stored as electrostatic potential energy(U) in the capacitor.
U=½q²/C = ½CV². (since q=CV)
This energy is recovered if the capacitor is allowed to discharge.
Capacitor is a charge storage device. Work has to be done to store the charges in a capacitor. This work done is stored as electrostatic potential energy in a capacitor.
Let q be the charge and V be the potential difference between the plates of the capacitor.If dq is the additional charge given to the plate, then work done is dw=Vdq
dw= q dq/ C. (since V=q/C)
Total work done to charge a capacitor is given by integrating dw
w= ½q²/C
This work done is stored as electrostatic potential energy(U) in the capacitor.
U=½q²/C = ½CV². (since q=CV)
This energy is recovered if the capacitor is allowed to discharge.
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