The voltage across a load is v(t) = 50cos( $ω$ t - 20 $°$ ) V and the current through the element in the direction of the voltage drop is i(t) = 2cos( $ω$ t + 70 $°$ A. Find the (a) real, reactive and apparent appa powers (b) power factor (c) load impedance (d) type of load.

Created: 3 weeks ago | Updated: 3 weeks ago

Updated: 3 weeks ago

(a) Real Power, $P = v_{r m s} i_{r m s} \cos (θ_{v} - θ_{i}) = \frac{50}{\sqrt{2}} \times \frac{2}{\sqrt{2}} \cos \{(- 20 °) - 70 °\} = 0 W$

Reactive Power, $Q = v_{r m s} i_{r m s} s i n (θ_{v} - θ_{i}) = \frac{50}{\sqrt{2}} \times \frac{2}{\sqrt{2}} \sin {\{(- 20 °) - 70\}}^{} = - 50 V A R$

Apparent Power, $S = v_{r m s} i_{r m s} = \frac{50}{\sqrt{2}} \times \frac{2}{\sqrt{2}} = 50 V A$

(b) Power factor, $p f = c o s (θ_{v} - θ_{i}) = c o s {(- 20 °) - 70 °} = c o s (- 90 °) = 0$

(d) As the reactive power is negative (Q = - 50VAR) and the impedance has a negative imaginary part (- j25) the load is purely capacitive (the current leads the voltage by 90 $°$ .