Solve RLC Circuit: Find Capacitor, Voltage, Power

[cool_stuff_lol]

Homework Statement

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

Homework Equations

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

 

[gneill]

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

 

[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.

 

[gneill]

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.

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.

 

[rezeew]

I would like to clarify that the values for the capacitor and voltage across the inductor may vary slightly depending on the precision of the given values and the calculations. However, the overall approach and equations used to solve the RLC circuit are correct. Additionally, it is important to note that the power consumed by the circuit is the total power consumed by all the components in the circuit, including the resistor, inductor, and capacitor. This power is calculated using the formula P=I^2R.