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Suppose the circuit in has a resistance of 15 ohm. Obtain the average power transferred to each element of the circuit, and the total power absorbed. |
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Answer» Solution :Here, `L = 80 MH = 80 xx 10^(-3) H, C = 60 MU F = 60 xx 10^(-6) , R = 15 ohm, E_(v) = 230 V, v = 50 Hz` `X_(L) = omega L = 2 pi v L 2 xx (22)/(7) xx 50 xx 80 xx 10^(-3) = 25.14 ohm` `X_(C ) = (1)/(omega C) = (1)/(2 pi v C) = (1)/(2 xx (22)/(7) xx 50 xx 60 xx 10^(-6)) = 53.03 ohm` `Z = sqrt(R^(2) + (X_(L) - X_(C )^(2))) = sqrt(15^(2) + (25.14 - 53.03)^(2)) = 31.67 ohm` `I_(v) = (E_(v))/(Z) = (230)/(31.67) = 7.26 A` Average power per cycle transferred to RESISTANCE `P_(R) = I_(v)^(2) R = (7.26)^(2) xx 15 = 790.6` watt Average power per cycle transferred to `L = P_(L) = 0` Average power per cycle transferred to `C = P_(C ) = 0` Total power per cycle absorbed, `P = P_(R ) + P_(L) + P_(C ) = 790.6` watt |
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