Alternating Current Essay

386 WordsMar 12, 20122 Pages
Alternating Current An alternating current or voltage reverses its direction regularly and is usually sinusoidal. We can represent the currnt and voltage by the equations : I = IOsinωt V = VOsinωt The time taken for one complete cycle of the a.c. is the period of the current T = 2π/ω. The reciprocal of the period is the frequency f ; that is, f = 1/T (f = ω/2π). The frequency is the number of complete cycle of the supply in one second. The unit of frequency is the hertz, Hz. The peak value of the current or voltage is IO or VO, the amplitude of the oscillating current or voltage. The averague value of an alternating current is zero. However, this does not mean that, when an a.c. source is connected to a resistor, no power is generated in the resistor. And alternating current in a wire can be thought of as electrons moving backwards and forwards, and passing on their energy by collision. The power generated in a resistance R is given by the formula : P = I2R but here the current I must be written as I=IOsinωt Thus P = IO2Rsin2ωt Because IO and R are constants, the average value of P will depend on the average value of sin2ωt, which is ½. So the average power delivered to the resistor is [ P ] = ½ IO2R = ½ VO2/R This is the half the maximum power. We could use the average value of the square of the current or the voltage in these relations, since [ I2 ] = ½ IO2 and [ V2 ] = ½ VO2 The squre root of [ I2 ] is called the root-mean-square or r.m.s., value of the current, and similarly for the voltage. The numerical relations are Irms = [ I2 ]1/2 = IO / (2)1/2 = 0.707 IO Vrms = [ V2 ]1/2 = VO / (2)1/2 = 0.707 IO The r.m.s. values are useful because they represent the effective values of current and voltage in an a.c. circuit. A direct current with a value of I equal to the r.m.s value that I quoted, not the peak value. The r.m.s. value of the

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