Calculating inductance and resistance of a coil from current and voltage

Question

I have the following question:

What I've done so far:

1. drew a vector diagram with the known voltages:
2. used the vector diagram to come up with 2 equations using pythagoras and used them to solve for BC and CD
3. calculated coil impedance from 180 V and 2.4 A and used that as the "resistance" part
4. calculated XL using the value I calculated for CD
5. calculated the phase difference using sin (VL/180), where VL is CD

My final answers are BC = 38.3 V; CD = 175.88 V; "R" = 75 ohm; XL = 73.28 ohm; phase difference = 77.72 deg. My 2 equations for BC and CD:

I'm pretty sure I went wrong somewhere but I can't figure out exactly where I went wrong. I THINK its in the calculation of CD, I can't remember where I got the 125 from. Any help would be appreciated!

Answer 1

There is a fault in your problem. If the total supply voltage is 240 volts then this is made up from the resistor voltage and the inductor voltage in series and in quadrature i.e.: -

Vtotal = \$\sqrt{V_R^2+V_L^2}\$ = \$\sqrt{90^2+180^2}\$ = 201.2 volts

This is not 240 volts so the problem in your question is flawed.