Answer to Question #172086 in Electrical Engineering for Classic em-ir

Question

if a frequency of 1mhz is applied across the circuit below find the inductor reactance of the circuit calculate the current flowing through each inductor as well as the voltage drop across each inductor if the voltage applied is 230v.what will the inductor reactance be.If the frequency was induced to 500 in the diagram are given, L1 2H,L2 1H,L3 5H,L4 500mH

Answer 1

Consider a circuit with 5 inductors connected in parallel:

The voltage across each resistor will be the same (as they are in parallel) 230 V.

The reactance of the circuit:

$$X=(X_1^{-1}+X_2^{-1}+X_3^{-1}+X_4^{-1}+X_5^{-1})^{-1},\\ X_i=\omega L_i=2\pi f L_i.$$

For equal values of X, we have

$$X=\frac{X_L}{5}=\frac25\pi f L=628.3\text{ k}\Omega.$$

The current in each resistor is

$$I_L=\frac{V}{X_L}=\frac{230}{628300}=366·10^{-6}\text{ A}.$$

The reactance of a single inductance at 500 Hz will be

$$X_{L500}=2\pi f_{500} L=1570\space\Omega.$$