- #1

Ben_Walker1978

- 113

- 6

- Homework Statement:
- RCL Series Network

- Relevant Equations:
- Ohms Law

Hello.

I have completed the following question.

My answer:

Reactance = XL = 2 x pi x F x L

= 2 x pi x 50 x 0.15

= 47.12 Ohms

Reactance of Capacitor = XC = 1/2 x pi x F x C

= 1/2 x pi x 50 x 80x10^-6

= 0.0006366 Ohms

Total reactance = XT = 47.12 - 0.0006366

= 47.119 Ohms

Z^2 = R^2 + XT^2

= 20^2 + 47.199^2

= 2,620.200161

Square Root of 2,620.200161 = 51.187 Ohms

Z = 51.187 Ohms

Theta = Tan^-1 (47.119/20) = 67 Degrees

Ohms Law

I = V/Z = 100/51.187

= 2.14 Ohms

0 Degree - 67 = -67 Degree

2.14 > -67 Degree

PF = True Power / Apparent Power

R = Resistance

Z = Impedance

PF = CosTheta = R/Z

= 20/51.187

= 0.390

I have this so far. Trying to learn and complete this question. Once i know these answers are correct i will draw the phasor diagram.

Any help will be much appreciated.

I think i have done all this correct. Just asking to make sure i haven't made any mistakes.

Thanks

I have completed the following question.

My answer:

**i)**

Circuit ImpedanceCircuit Impedance

Reactance = XL = 2 x pi x F x L

= 2 x pi x 50 x 0.15

= 47.12 Ohms

Reactance of Capacitor = XC = 1/2 x pi x F x C

= 1/2 x pi x 50 x 80x10^-6

= 0.0006366 Ohms

Total reactance = XT = 47.12 - 0.0006366

= 47.119 Ohms

Z^2 = R^2 + XT^2

= 20^2 + 47.199^2

= 2,620.200161

Square Root of 2,620.200161 = 51.187 Ohms

Z = 51.187 Ohms

Theta = Tan^-1 (47.119/20) = 67 Degrees

**ii)****Circuit current**Ohms Law

I = V/Z = 100/51.187

= 2.14 Ohms

0 Degree - 67 = -67 Degree

2.14 > -67 Degree

**iii)**

The Power Factor

The Power Factor

PF = True Power / Apparent Power

R = Resistance

Z = Impedance

PF = CosTheta = R/Z

= 20/51.187

= 0.390

I have this so far. Trying to learn and complete this question. Once i know these answers are correct i will draw the phasor diagram.

Any help will be much appreciated.

I think i have done all this correct. Just asking to make sure i haven't made any mistakes.

Thanks