CAPACITANCE ( DEFINITION, ARRANGEMENT AND APPLICATION)

CAPACITANCE`(DEFINITION, ARRANGEMENT AND APPLICATION)

A capacitor is a device for storing electric charges or for storing electricity. It consists essentially of two conductors (metal plates) carrying opposite charges. The metal plates are separated a small distance, d, by an insulator.

The insulating material placed between the plates of a capacitor is called dielectric substance. The capacitance increases with the area between the plates, decreases with increasing distance, and increases with dielectric constant.

The Capacitance (C ) of a capacitor is defined as the ratio of the charge Q on either plates or conductors to the potential difference V between them.

C =  . The unit of capacitance is the Farad. The capacitance of a capacitor is one farad if one Coulomb of charge is transferred from one conductor to the other per unit volt of potential difference between the conductors.

Quantitatively, the capacitance of a capacitor is a measure of its ability to store up electricity. The capacitance, C is a constant for a given capacitor.

Factors affecting the capacitance of a parallel-plate capacitor.

The value of capacitance depends on the size, shape, distance separating the two plates, and the nature of the material that separates them and the common area of plates.

Capacitors in series and parallel.

The resultant or equivalent capacitance of any number of capacitors connected in parallel is the sum of their individual capacitances. The reciprocal of the equivalent capacitance of any number of capacitors connected in series is the sum of the reciprocals of the individual capacitances.

Capacitors in series

 =  +  +

Capacitor in parallel

C =  +  +

Energy stored in a charged capacitor.

This work done in charging a capacitor is the energy stored in the capacitor. Hence

W = qV =  =

W is in joules if q is in coulombs, V in volts and C in farads.

Application of Capacitors

Used of capacitors  are: i. Radio circuits for turning  ii. Ignition system of motor vehicles.

iii. The elimination of sparks when a circuit containing inductance is suddenly opened e.g in induction coils.

Example

1.  A work of 30 joules is done in transferring 5 milliCoulombs of charge from a point B to a point A in an electric field. The potential difference between B and A is.

Solution

W= 30J, q= 5x10-3C, V =?

W = qV ; V =  =  = 1.2 x104V

2. A series arrangement of three capacitors of value 8ᶙf, 12 ᶙf, and 24 ᶙf is connected in series with a 90-V battery. (i) Draw an open circuit diagram for this arrangement. (ii) Calculate the effective capacitance in the circuit. (iii) On close circuit, calculate the charge on each capacitor when fully charged. (iv) Determine the p.d across the 8 ᶙf capacitor.

Solution

(i)

 

 

 

(ii)  =  +  +

   =  +  +  ;   =  ;   =  ; C= 4 ᶙf

(iii) charge on 8 ᶙf = charge on 12 ᶙf capacitor

(iv) Total charge, Q, = CV = 4x10-6F x 90V = 3.6 x 10-4C

p.d across the 8 ᶙf capacitor =  =  = 45V

 

  

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