Question

The following Table gives the reactance and rms voltage across the elements of a series RCL circuit, what is the rms current in the circuit?

Circuit element, reactance, voltage across element
resistor, 200 ohm, 86V
capacitor, 663 ohm, 285V
inductor, 377 ohm, 162V

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I have .43A as the answer from an online source but am getting .30A when I do it. I do the following:

I_rms = V_rms/Z
V_rms = V_0/sqrt(2)
V_0=sqrt(V_r^2+(V_l-V_c)^2)=150.08
Z=sqrt(R^2+(X_l-X_c)^2 = 348.992

if someone could point out my mistake I would be grateful. Thanks

Answer 1

This will surprise you how it can be solved. First it is a series circuit and current is the ideal reference as in a series circuit, current is the same. The resistor will have a voltage drop (given as 86 volts) which will be in phase with this current. So the resistor is the key.

i=e/r
i=86/200=.43A The other elements have a phase difference between their voltage and their current as they are reactive.

Answer 2

Note that overall the circuit appears capacitance with the resultant voltage lagging the current.