A 200 Ω resistor and a 50 Ω X_{L} are placed in series with a voltage source, and the total current flow is 2 amps, as shown in Figure.

Figure : Series R-L Circuit

Find:

- Power Factor, pf
- Applied voltage, V
- True Power, P
- Reactive Power, Q
- Apparent Power, S

**Solution:**

**1. Calculate Power factor (pf)**

p.f. = cos (14º)

p.f. = 0.097

**2. Calculate Applied Voltage, V**

**V = I Z**

**Z = √R ^{2} + X_{L}^{2}**

so,** V = I****√R ^{2} + X_{L}^{2}**

V = 2√200^{2} + 50^{2}

V = 2√42500

V = 2 x 206.16

V = 412.3 Volts

**3. Calculate True Power, P**

**P = EI cos θ**

P = (412.3)(2)(0.97)

P = 799.86 watts

**4. Calculate Reactive Power, Q**

**Q = EI sin θ**

Q = (412.3)(2)(0.242)

Q = 199.6 VAR

**5. Calculate Apparent Power, S**

**S = EI**

S = (412.3)(2)

S = 824.6 VA