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The variation of inductive reactance (X_(L)) of an inductor with the frequency (f) of the a.c. source of 100 V and variable frequency is shown in the figure. (i) Calculate the self-inductance of the inductor. (ii) When this inductor is used in series with a capacitor of unknown value and a resistor of 10Omega at 300 s^(-1), maximum power dissipation occurs in the circuit. Calculate the capacitance of the capacitor. |
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Answer» Solution :(i) As per `X_(L)` -f graph for a frequency f = 100 Hz , `X_(L) = 20 Omega` `:. X_(L) = L omega = L.2pif ` `IMPLIES L = (X_(L))/(2pif) = (20)/(2xx3.14xx100) = 0.032 H or 32 ` mH (ii) As at a frequency `f_(0)=300 s^(-1)` maximum power dissipation occurs the frequecny `f_(0)` is the resonant frequency . We KNOW that `f_(0) = (1)/(2pisqrt(LC)), so C = (1)/(4pi^(2) f_(0)^(2) L) implies C = (1)/(4xx(3.14)^(2)xx(300)^(2)xx0.032) =8.85 F` |
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