A variable inductor with negligible resistance is connected to an ac voltage source. By what factor does the current in the inductor decrease if the inductance is increased by a factor of 6.0 and the driving frequency is increased by a factor of 8.0?
Assuming that the voltage source is sweet, i.e., has 0 sequence impedance, and there are no longer the different elelements in the circuit, the present in direction of the inductor would be V / Z? the place V is the voltage of the source, it incredibly is additionally the voltage around the burden inductor, and Z? is the impedance of the inductor, with Z? Rs + j?L, the place Rs is the equivalent sequence resistance of the inductor, which in this occasion is negligible, ? is the angular frequency of the excitation, it incredibly is 2? circumstances the employing frequency f, and L is the inductance. The j is for sure the significant root of -a million. Neglecting the resistive element, the magnitude of the present will hence be V / (2?fL) If fo is the unique frequency and Lo the unique inductance, the present after the ameliorations in frequency and inductance would be V / [2?(4fo)(Lo/8)] V / [2?foLo*(4/8)] 2 V / (2?foLo) so the present will boost with the help of part of two.
X wL where X is the inductor's Reactance and w is the frequency in rads/sec the reactance will increase by 6 x 8 48 so the current will decrease by the same factor
