Evaluate Phase difference between voltage and current:

An inductive coil of reactance 15.7 Ω and resistance 32 Ω is connected in series with a capacitor of reactance 79.5 Ω. The circuit is connected across 500 V AC supply, Find out

1. Current,

2. Phase difference between voltage and current,

3. Magnitude of voltage across the inductive coil, and

4. Total power absorbed.

Solution

Figure for Example

R = 32 Ω,         X = XL - XC

= - 63.8 Ω (circuit in capacitive)

Impedance      Z = R - jX = 32 - 63.8 j Ω

(a) Current i =  v / Z  = 500 ∠ 0^o / 32 - 63.8 j

                            = 7 ∠ 63.36o Amp

(b) Angle between V and i

                   φ = 63.36 (leading)

(c) Impedance of coil, Z_L = R + j X_L = 32 + j 15.7

| Z _L | = 35.6439 Ω

Voltage across coil = I Z_L = 7 × 35.6439

                                    = 249.5075 Volt

(d) Power absorbed = I² R = 7² × 32 = 1568 watts