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7, HEATING EFFECT OF CURRENT, Heating Effect of Current, , When a potential difference is maintained, across the ends of a conductor then an electric field, comes into action inside the conductor from its higher, Potential and to its lower potential end. Under the, effect of electric field the free electrons present inside, the conductor experiences electric force in the direction, opposite to the electric field and they begin to, , * accelerate in the direction opposite to the electric field., Thus, the free electrons acquire speed and hence K.E., due to the work done by the electric force. During their, motion the collision of free electrons takes place with, the +ve ionic loses present inside the conductor and, transformation of their K.E. takes place into heat, energy., , The phenomenon of generation of heat energy is, the conductor when electric current is allowed to from, through it is called heating effect of current., , , , Expression of Heat Generated, , Consider a conductor of resistance R in which, flow of electric current J takes place when a potential, difference V is applied across is it., , Then, the charge which flow through any crosssection of conductor in time ¢ is given by, , qz=lIt, , By def. the work done in moving a unit positive, charge from one end of the conductor to the other end, is equal to the potential difference across the, conductor., , Therefore, the work done is moving g amount of, , charge from one end of the conductor to the other end, , , , As the amount -of heat generated is directly, proportional to the work done by the electric field (or, , by the source of e.m.f.), ie. W«H, , or W = JH, where J is Joule's mechanical equivalent of, heat and its value depends upon the units of W& H., , , , Ww, wey, vit_I’Rt V?t, or Hey RT, If W is Joule and H is in calorie then, J= 4.186 = 4,2, cal cal, 2 2, H = Vit _U'Rt_ vit, , 42 42 42R, If W isin erg and H isin caloric then, , J = 4186x107 28 -4.2x107 2, cal cal, , _ _ Vit Rt _ vt, 4.2x107 4.2x107 4.2x107, , and if W and H both are in the same units, then, J=!I, , y2, H = Vit=I°Rt=——t, R, , Note ; Appliances like electric bulb, electric, iron, electric heater etc., works on the principle of, heating effect of current., , Joule's Law of Heating Effect of Current, , In the year 1841 on the basis of his experiments, related to heating effect of current, Joule enunciated, three laws which are known as Joule's law of heating., , (1) First Law or Law of Currents : When, different amounts of electric current are allowed to, flow through the same resistor for a given time, interval then the amount of heat generated is directly, , , , in given by proportional to the square of electric current., W=qVv ie, H«l? (R and ¢ constant], or W-mv teq=lt] (2) Second Law or Law of Resistance : When, Wie VE the same amount of electric current is allowed to flow, ‘ mf \ 5 through different resistances for a given time interval, “By Ohm'slaw V = IR than the amount of heat generated is directly, a W = (IR)It Proportional to the resistance of resistor., or W = I?Rt ie. H«R (Zand ¢ constant], I oR (3) Third Law or Law of Time : When the, i - ji i, A B same amount of electric current is allowed to flow, through the same resistor for different time intervals, av than the amount of heat generated is directly, ‘a I= v Proportional to the time interval., SO -R ie. He«t {I and R constant}, vy Combining all the above three laws, We (¥) Rt H = I?Rt, y? or H = KI’Rt, or We Re where K -+ is a constant of proportionality, “Wisa Computers : 9826238548 a (Class-XII), , Scanned with CamScanner

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PR, J, where «J is Joule's mechanical equivalent of, heat and its value depends upon the units in which, H,I,R and t are taken,, , If H is in calorie, I is in ampere, R is in ohm, and ¢ isin second., , H=, , , , Then, J = 4.92., cal, 2, He I’Rt, 42, , Electric Power, , The rate of which work is done by the source of, , ’ em.f. in order to maintain the flow of electric current, , an electric circuit is called electric power of that, source,, , In other words, the rate at which the electrical, energy is supplied by the source of e.m.f. in order to, maintain the flow of electric current in an electric, circuit is called electric power of that source., , If the work done by the source of e.m.f. in order, to maintain the flow of current in an electric circuit for, time ¢ be W. Then, the electric power of source of, e.m.f. is given by, , p=, t, 2, W = vit=PRt= 4, R, y2, 01 P = Vt=I?R=—, R, , It is scalar quantity. Its SI unit is watt, CGS, unit is ergs“! and dimensional formula is [ML?T~*),, Note : Electric power is also defined for electric, circuit in the following manner :, The rate at which work is done in an eleetric, circuit., Or, , The rate at which electrical energy is supplied to, the electric circuit., , Or, The rate at which dissipation of heat takes in an, electric circuit., , Definition of SI Unit of Power, , In relation, P=VI, If V = 1VandI=1A, Then P = 1V-1A=1W, , Thus, if on applying a potential difference of 1V, across an electric circuit the electric current flowing, through it be 1A then its electric power is said to the, iW., , Note : Other units of electric power, 1kW = 10°W,1MW =10°W, 1HP = 746W, , ", , and, , , , Definition of kWhr and its Relation with Joule, , Ww, From relation Pe — we have, W = Pt, If P = 1kW and ¢ = lhr, then W = 1kWxih, = 1kWh, , Thus, 1kWh is the electrical energy consumed, in lhr in a electric circuit whose power is 1kW., , It is the commercial unit of electrical energy and, it is also called unit., , Relation Between kWh and Joule, , 1kWh = 1hWx 1h, , 10° W x 3600s, 3.6 «1097, Calculation of No. of Units (kWh), , ", , If an applying a potential difference V across a, conductor the electric current flowing through it be J, then the electrical energy consumed in it in time ¢ is, given by, , W = Vit, , It V isin volt, 7 is in ampere and ¢ is in hour,, , then, , W ‘= V(volt) x (amp) x t(hr), or W = VI (volt-amp) xt (hr), or W = P(watt)xt(hr), oe We P(watt) x t(hr), , 1000, (in kWh), No. of unite = P(watt) x t(hr), 1000, , , , [Class-XII) @), , Nisa Computers: 9826238548, , Scanned with CamScanner