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Home , Ohm, Siemens (unit)

BASIC

BY: KUMAR AVINASH CHANDRA GUEST FACULTY Email: [email protected] Contact: +91 7837 11 4644 DR. A.P.J.A.K. W. I. T., DARBHANGA ELECTRIC CIRC U IT

• An electric circuit is a closed path consisting of active and passive elements all interconnected and the current flow is confined to the closed path. • An Active element is one which supplies energy to the circuit where as a Passive element is one which receives energy and then this energy is converted into heat () or stores it in an electric (capacitor) or magnetic field (inductor).

• The basic unit of charge is the charge on an electron. The mks unit of charge is . An electron has a charge of 1 .062 x l0-19 C. • An electric current is defined as the time rate of flow of charge through a certain section. Its unit is . • A current is said to be of one ampere when a charge of 1 coulomb flows through a section per .

• Mathematically, i = 푑푞 푑푡 ELECTRIC POTENTIAL

• The movement of charges contribute to current and the amount of work done per unit charge is the potential difference between the two points. • The electronic charges flow from a lower potential to a higher potential and these contribute to electronic current, whereas the conventional current is considered to flow from higher potential to lower potential. • If a differential charge dq is given a differential energy dw, the rise in potential of the charge. Mathematically, v = 푑푤. 푑푞 • The units of potential or potential difference as derived from equation are /coulomb or s termed as . RESISTANCE

• A insulator is one which opposes the flow of current. • The derived units for resistance is , its quantity symbol is and the unit symbol is Q. The unit for electric resistance is defined as R = 푉 (r = 푉 ) 퐼 퐴 • If the potential difference between point a and b is say 1 V when the current in the circuit is 1 A, the resistance between points a and b is said to he of 1 Q. • A circuit element designed to have property of resistances is known as a resistor and its circuit symbol is shown in Fig RESISTIVITY

• The value of resistances R of a conductor is directly proportional to its lengths

i.e. R oc l

푙 Also, if the cross sectional area of the cylindrical wire is varied, the resistance is found to be inversely proportional to the cross-sectional area A i.e. R oc Τ퐴 These two proportions can be combined and we have

R oc 푙 퐴 and by using a constant of proportionality p the proportion becomes the equation and

R = p 푙 Ω 퐴 In order to find the units for p we substitute the units of other quantities

Ohm = p 푙푒푛𝑔푡ℎ = p 푚푒푡푟푒 퐴푟푒푎 푚푒푡푟푒2 or p = Ohm-

Thus p, the resistivity of the material or specific resistance is the resistance of a material measured between opposite forces. CONDUCTIVITY AND CONDUCTANCE

• The specific resistance or resistivity p of a material represents its opposition to the flow of electric current. However the reciprocal of p represents a unit describing the material in terms of its ease to allow flow of electric current. y = 1/p known as the conductivity of the material. Similarly, the reciprocal of resistance R is the conductance G i.e. G = 1/R. The SI derived units for conductance from Table i. 1 is the . The quantity symbol is G and the unit symbol is S. The Siemens is derived as G A = V , S, where A is . Conductance also given in mho and its symbol . However, the use of unit mho must be avoided and Siemens should be used.

If potential is multiplied by current 푑푞, we have 푑푡

V x I = 푑푊 * 푑푞 = 푑푊 푑푞 푑푡 푑푡 which gives rate of change of energy with time and is equal to power. The SI derived unit for power (P) is expressed as Joule per sec. ENERGY

We have,

P = 푑푊 푑푡 dW = Pdt = VI dt W = VI dt and energy of a device is defined as the capacity of doing the work and its derived unit is -sec. THANKYOU

Email: avinas[email protected] Contact: +91 7837 11 4644 Next Topic: Ohm’s Law