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www.GOALias.blogspot.comPhysics7.2 AC VOLTAGE APPLIED TO A RESISTORFigure 7.1 shows a resistor connected to a source ε ofac voltage. The symbol for an ac source in a circuitdiagram is ~ . We consider a source which producessinusoidally varying potential difference across itsterminals. Let this potential difference, also called acvoltage, be given byv = vmsin ωt(7.1)where v mis the amplitude of the oscillating potentialdifference and ω is its angular frequency.NICOLA TESLA (1836 – 1943)234Nicola Tesla (1836 –1943) Yugoslov scientist,inventor and genius. Heconceived the idea of therotating magnetic field,which is the basis ofpractically all alternatingcurrent machinery, andwhich helped usher in theage of electric power. Healso invented among otherthings the induction motor,the polyphase system of acpower, and the highfrequency induction coil(the Tesla coil) used in radioand television sets andother electronic equipment.The SI unit of magnetic fieldis named in his honour.FIGURE 7.2 In a pureresistor, the voltage andcurrent are in phase. Theminima, zero and maximaoccur at the samerespective times.To find the value of current through the resistor, weapply Kirchhoff’s loop rule ∑ ε () t = 0, to the circuitshown in Fig. 7.1 to getv sin ω t = iRmFIGURE 7.1 AC voltage applied to a resistor.v mor i = sin ω tRSince R is a constant, we can write this equation asi = imsin ω t(7.2)where the current amplitude i mis given byvmim= (7.3)REquation (7.3) is just Ohm’s law which for resistors worksequally well for both ac and dc voltages. The voltage across apure resistor and the current through it, given by Eqs. (7.1) and(7.2) are plotted as a function of time in Fig. 7.2. Note, inparticular that both v and i reach zero, minimum and maximumvalues at the same time. Clearly, the voltage and current are inphase with each other.We see that, like the applied voltage, the current variessinusoidally and has corresponding positive and negative valuesduring each cycle. Thus, the sum of the instantaneous currentvalues over one complete cycle is zero, and the average currentis zero. The fact that the average current is zero, however, does