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www.GOALias.blogspot.comPhysicsThe large scale transmission and distribution of electrical energy overlong distances is done with the use of transformers. The voltage outputof the generator is stepped-up (so that current is reduced andconsequently, the I 2 R loss is cut down). It is then transmitted over longdistances to an area sub-station near the consumers. There the voltageis stepped down. It is further stepped down at distributing sub-stationsand utility poles before a power supply of 240 V reaches our homes.SUMMARY1. An alternating voltage v = v sin ω t applied to a resistor R drives amvmcurrent i = i msinωt in the resistor, im= . The current is in phase withRthe applied voltage.2. For an alternating current i = i msinωt passing through a resistor R, theaverage power loss P (averaged over a cycle) due to joule heating is(1/2)i 2 R. To express it in the same form as the dc power (P = I 2 R), amspecial value of current is used. It is called root mean square (rms)current and is donoted by I:imI = = 0.707im2Similarly, the rms voltage is defined byvmV = = 0.707vm2We have P = IV = I 2 R3. An ac voltage v = v msinωt applied to a pure inductor L, drives a currentin the inductor i = i msin (ωt – π/2), where i m= v m/X L. X L= ωL is calledinductive reactance. The current in the inductor lags the voltage byπ/2. The average power supplied to an inductor over one complete cycleis zero.4. An ac voltage v = v msinωt applied to a capacitor drives a current in thecapacitor: i = i msin (ωt + π/2). Here,vm1i = m, XCX= CωCis called capacitive reactance.The current through the capacitor is π/2 ahead of the applied voltage.As in the case of inductor, the average power supplied to a capacitorover one complete cycle is zero.5. For a series RLC circuit driven by voltage v = v msinωt, the current isgiven by i = i msin (ωt + φ)vmwhere im=2R + X − Xand φ = tan−1XC− XR( ) 2LCL262( ) 22Z R XCXL= + − is called the impedance of the circuit.