# RLC circuit

1. Nov 16, 2013

### cool_stuff_lol

1. The problem statement, all variables and given/known data

A series RLC circuit consists of resistor of 200Ω, an inductor of 0.214H and a capacitor of unknown value. When this circuit is energized by 240∠0°, 50Hz sinusoidal supply, the current was found to be 2.6∠0° amperes. Determine:

(i) Value of capacitor in microfarad
(ii) Voltage across the inductor
(iii) Total power consumed

2. Relevant equations

3. The attempt at a solution

(i) arctan 0°=(χL-χC)/R
χC=χL
χC=2*pi*50*0.214=67.23Ω

C=1/(2*pi*50*0.214)=47.3μF

(ii) V=2.6*67.23=174.8V

(iii) Power= 200*(2.6)^2=1.35kW

2. Nov 16, 2013

### Staff: Mentor

Did you have a question about your solution? The results look fine.

3. Nov 16, 2013

### cool_stuff_lol

I had a doubt regarding the impedance of the circuit. If the current and voltage are in phase with each other shouldn't the impedance equal the value of the resistor? However, the impedance is less than the value of the resistor using Z=V/I.

4. Nov 17, 2013

### Staff: Mentor

True. We'll have to conclude that the problem statement is not accurate. Perhaps there's a typo or someone changed the values at some point to make a "new" question.

But your approach is correct if the voltage and current are in phase.