CBSE Class 12 Physics Capacitance Theory and Examples

CBSE Class 12 Physics Capacitance Theory and Examples. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

1.CAPACITANCE
(i) When a conductor is given a charge , it's potential rises in proportional to the charge given i. e.
Q ∝ V or Q = CV or C = Q/V
This C is a constant and is called the CAPACITANCE of conductor

(ii) Electrical capacitance of a conductor is a measure of it's ability to hold electric charge.

(iii) A given conductor can be charged to a limit. Charging after the limit results into ionization of medium, and charge gets leaked into medium

(iv) C depends on
(a) Size and shape of conductor
(b) Surrounding medium
(c) Presence of other conductor near by
(v) Units(1) Coulomb/volt

(2) Farad
1 Farad = 1 Coulomb/volt.

(vi) If potential of a conductor rises by 1 volt as a result of charging by 1 coulomb , then capacitance of that conductor is said to be 1 Farad.

(vii) The farad is too large a unit (spherical conductor of 1 farad must have a radius of 9 × 108m). Hence in practice these units are used -
1μF = 1 × 10^–6 F
1nF = 1 × 10^–9 F
1pF = 1 × 10^–12 F

(viii)Dimension[M^-1 L^-2 T⁴ A²]
(ix) CGS unit : 9 × 10¹¹ statfarad = 1 Farad

Capacitance

Ex.1 A conductor gets a charge of 60 pC when it is connected to a battery of emf 6 mV. Then the capacitance of the conductor is...........
(A) 120 × 10^–6 (B) 1.2 × 10^–9 (C) 10 × 10^–9 F (D) 10 × 10^–6 F
Sol. The definition of capacitance is
C =Q/V= 60×10^-12/60×10^-3 = 10^–8 F
Ans.[C]

Ex.2 Farad is not equivalent to-
(A)Q/V  (B)  VJ/2  (C)Q2/J D) CV²

Sol. [C =Q/V=Q²/VQ=Q²/J

and C =Q/V =QV/v₂= J/v²

Ans.[D]

1.1 Capacitance of an isolated spherical conductor
Q : Charge on the sphere
V : Potential at the surface of sphere
R : Radius of sphere

⇒ ε0 = C/4π R
⇒ units of ε0 = Farad/meter

Note: C²/N -m² is another unit of ε0 .Thus F/m and C²/N -m² both represent the same physical quantity.

Ex.3 Can a sphere of radius 1 cm, placed in air be given a charge of 1 coulomb.
Sol. Potential of sphere of 1 cm radius is.
V = k qr
= 9 × 10⁹ × 1/10^-2

= 9 × 10¹¹ volt

This potential is so high that the surrounding air gets ionized, thereby charge leaks to the medium.[Air gets ionized at 3 x 10⁶ volt]
Ans. [No]

Ex.4 Two spheres, one being hollow and another solid, have equal radius. If they are charged to V volt, then which one will acquire more charge.
Sol. Both will acquire same charge
∴ C ∝ R, the capacitance of both the
spheres is same, so charge will be same on both. [ ∴ Q = CV]

Ex.5 If the diameter of earth is 128 × 102 km, then its capacity will be-
(A) 111 μF (B) 211 μ F (C) 331 μ F (D) 711 μ F
Sol. C =R/K = 64 x 10⁵/ 9 x10⁹ = 711 μF
[where k =1/4πε₀ ]

Ans.[D]

Ex.6 64 water drops having equal charges & equal radius combine to form one bigger drop. The capacity of bigger drop, as compared to that of smaller drop will be-
(A) 8 times (B) 64 times (C) 4 times (D) 16 times
Sol. Q 34πR³ = 64 × 34πr³
⇒ R = 4r
⇒ 4πε₀R = 4 × 4πε₀r
⇒ C_Bigger = 4 C_smaller
Ans.[C]

Ex.7 Capacity of a metal sphere will be 1 μf , if it's radius is nearly -
(A) 9km (B) 64 km (C) 81 km (D) None of these
Sol. C = 4πε₀R = 1μF
R =10⁶/4πε₀
= 9 × 10⁹ × 10^–6 = 9km
Ans.[A]

Ex.8 A radioactive source in the form of a metal sphere of diameter 10^-3 m emits β paraticles at a constant rate of 6.25 × 10¹⁰ particles per second. If the source is electrically insulated, how long will it take for its potential to rise by 1.0 volt, assuming that 80% of emitted β Particles escape from the surface.
Sol. Capacitance of metal sphere of radius
r = 0.5 × 10^–3 m

2. ENERGY OF A CHARGED CONDUCTOR

(i) The work done in charging the conductor gets stored as potential energy in the electric field in the vicinity of the conductor.
(ii) Suppose, a conductor is given a charge q, then potential of conductor = V = q/c Work done to bring a further charge dq is given by dw = Vdq = q/C dq So, work done to charge it from 0 to Q is

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