Determine Impedance - Resultant current and Power factor:

In series R-L circuit, illustrated in Figure , Determine

1.      Impedance,

2.      Resultant current,

3.      Power factor and its nature, and

4.      Quality factor.

Figure

Solution

The inductive reactance XL is given by

XL = ωL

= 2π fL

= 2π × 50 × 0.1 Ω

= 31.42 Ω

The impedance in rectangular form is given by

Z = R + j X L  = 10 + j 31.42 Ω

In polar form   Z = 32.97 ∠ 72.345^o Ω

The resultant current is given by

i = ν / Z = 220 ∠ 0^o / 32.97 ∠ 72.345^o

= 6.672 ∠ - 72.345^o Amp.

The current is lagging (since the circuit is inductive).

The power factor angle, φ, is the angle between voltage current

φ = 72.345^o (lagging)

∴          p.f. cos φ = cos (72.345^o)

= 0.303 (lag)

On the other hand, the power factor may be determined by

cos φ = R/ Z

=          10 /32.97

= 0.303 (lag)

Quality factor is given by Q = 1/ cos φ = 3.3 .