are connected to 240V 50 Hz AC mains. a current of 3A flows lagging 31degrees behind the supply of voltage while the voltage across the inductor is 171V.determine the resistance and inductive reactance.
If I told you how long ago it was when I last did problems like this you wouldn`t believe me! However I am tempted to have a go. For calculation purposes , let 3A current lag by 30 ° rather than the 31 ° you suggest. Also let voltage across inductor be 170 V Vr ? 240 ? - 170 ? Vr 170 V (voltage across resistor) 170/3 R 57? let inductive reactance X ? Voltage across inductance 170 v I 170 / X 3X 170 X 57? I will be pleasantly surprised if this is correct !
Resistance W/A^2 [(240V)*(3A)*(cos 31 degrees)] /(3A^2) 617.1604365 / 9 68.57 Ohms Inductive reactance (tan 31 degrees)*(68.57 Ohms) 41.2 Ohms Note: The given Voltage of 171V across the inductor does not correlate with the other given data. Voltage across inductor (inductive reactance)* (current) (41.2 Ohm)*(3 Amps) 123.6 Volts Source Voltage (inductor Voltage) / (sin phase angle) 123.6V / sin 31 degrees 240 Volts which agrees with the given source Voltage. Therefore the 171V given across the inductor must be incorrect.
Assuming the inductor contains no contemporary or voltage earlier the swap is closed. whilst the swap is then closed, provided that no instant contemporary can bypass (provided that contemporary earlier the swap became 0, merely after the swap is closed it nevertheless ought to be 0 - e.g. contemporary can no longer exchange today with the aid of an inductor) the inductor on the instant assumes a voltage (i.e. a back emf) equivalent in value, yet opposite in polarity to the battery. This ought to be with the intention to fulfill the closed circuit loop situations; that's, the only way the present may well be 0 merely after the swap is closed is to have 0 potential around the circuit loop, meaning the inductor straight away obtains a 'back emf' potential. Then, after an infinitesimal time, the present starts off to bypass and the inductor emf collapses to 0, wherein the inductor emf/voltage is then 0, however the present flowing interior the circuit loop is then maximum. the present obtains its maximum value of V/R (the place Vbattery voltage) purely whilst the inductor emf is 0! it is vital to the know-how of the physics! provided that inductors and capacitors are passive gadgets (i.e. they can't furnish power to the circuit on their very own accord), they might purely keep power and this might purely be performed if the voltage and contemporary are disjoint (e.g. in 'quadrature').
