Electric capacitors:
- Capacitors are charge storing devices.
- Capacitance of a capacitor is the ratio of charge(Q) given and the potential (V) to which it is raised. C=VQ
- The SI unit of capacitance is Farad and its CGS unit is Stat farad.
- 1 stat farad = 91∗10−11farad
- The dimensional formula of electrical capacitance is [M−1L−2T−4A−2]
- The capacitance of spherical conductor is : C=4πEoR=9∗109R where R is the radius of the conductor.
- The capacitance of concentric spherical capacitor is: C=4πEob−aabwhere 'b' is the radius of outer sphere and 'a' is the radius of inner sphere.
- The capacitance of the earth is 7.12∗10−4 farad = 712μF
Parallel plate capacitor:
- It is the simplest capacitor where two conductors are separated by insulator/dielectric.
- The capacitance is given by: C=dEoA=dKEoAwhere A is the area of each plate, d is distance between them and K is the dielectric constant.
- The capacitance does not depend on material of plates, charge given to plates, potential difference between the plates.
- The value of C depends on size, shape and relative position of the two coatings of the capacitor. It also depends on the medium separating the two coatings.
- When the space between the plates is partially filled with medium of dielectric constant K and thickness t then capacitance becomes: C′=d−t(1−K1)EoA
Combination of capacitors:
- Series combination: C1=C11+C21+.........Cn1
- Parallel combination: C=C1+C2+........Cn
Dielectric in series:
- The capacitance of a parallel plate capacitor having a number of slabs of thickness t1,t2,t3,.....and dielectric constants K1,K2,K3,....... respectively in between is: C=K1t1+K2t2+K3t3+......EoA
Dielectric in parallel:
- When a number of dielectric slabs of same thickness(d) and different areas of cross section A1,A2,A3,.... having dielectric constants K1,K2,K3,........respectively are placed between the plates of a parallel plate capacitor, its capacitance is given by: C=dEo(K1A1+K2A2+K3A3+.....)
Energy stored in a capacitor: U=2CV2=2qV=2Cq2
Energy density: UE=2EoE2where E is the electric field intensity
Some important relations:
- Regrouping of capacitors:
- When like plates are joined:
C1V1+C2V2=(C1+C2)V
V=C1+C2C1V1+C2V2
Loss in energy = 2(C1+C2)C1C2(V1−V2)2
- When unlike plates are joined:
V=C1+C2C1V1−C2V2
Loss in energy = 2(C1+C2)C1C2(V1+V2)2
- For charging a capacitor:
q=qo(1−eRC−t)
V=Vo(1−eRC−t)
I=IoeRC−t
- For discharging a capacitor:
q=qoeRC−t
V=VoeRC−t
I=IoeRC−t