# What's the correct approach to this RLC circuit problem about RMS voltage?

How are you supposed to determine $$\V_{C,RMS}\$$ without R, L or C?

I drew a phasor diagram and used $$\Z=\sqrt{R^2+(X_L-X_C)^2}\$$ but am unsure on how to proceed from here as I do not have values of R, L or C.

• Draw the phasor diagram. – Charles Cowie Feb 20 at 0:57
• I did, and using Pythagoras' Theorem I would be able to find the impedance and then the RMS current, but the problem is I don't know R, L or C to help me find those. – Kevin Feb 20 at 1:01
• Please tag this as homework and then provide your working so far so we can help. – mhaselup Feb 20 at 1:02

Basic LCR rule Vs=SQRT((Vl-Vc)^2+Vr^2) plus some algebra. This should be in the first few paragraphs of the LCR in series chapter of any AC theory textbook.

Have a look here... Page 3 has the information you need to solve this problem with only the voltages. learnabout-electronics.org/Downloads/ac_theory_module09.pdf

Also here... https://byjus.com/physics/lcr-circuit/

This is a series resonant circuit. The reactive impedance of the capacitor is subtracted from that of the inductor.

You have the voltages for the overall circuit, the resistor and inductor. Since the voltage is proportional to the resistance/reactances you effectively know the information you need to know to do the calculation.

Draw a diagram of the overall circuit voltages i.e. 200, 100 and deduce the voltage due to combined reactance (of L and C) from that. It is 173.2 volts.

Now calculate voltage across the capacitor (bearing in mind the combined reactance is that of the inductor minus the capacitor).

This is essentially an algebra problem involving square roots. It may have more than one answer. It is also a series RLC circuit. The current is the same flowing through all three components.

The phasor voltages add vectorially to give the line voltage which is 200 volts rms.

In other words : sqrt( (resistive voltage)^2 + (total reactive voltage)^2 ) = total line voltage

The total reactive voltage is: coil voltage - capacitor voltage.

When the total equation is solved there are two answers: 123 volts and 223 volts. The solution is found by plugging both voltages into the original equation. The wrong voltage will not give the correct answer. The other answer, 223 volts RMS, is the correct capacitor voltage. That the total reactive voltage is negative indicates a capacitive circuit.