Question

A voltage source 𝑣(𝑡) = 240 sin(314.16𝑡 − 20°)𝑉 is connected to a load having an

impedance of Z. The resulting current through the load is 𝑖(𝑡) = 15 sin(314.16𝑡 + 22.5°)A.

Determine the circuit power factor and identify the elements that constitute the load, given

that Z comprises of only two elements connected in series.

Answer 1

i leads the v (voltage). This is possible for the capacitive loads.

Therefore given load is resistor and capacitor load.

$R=|Z|cos \phi = 16 cos -42.5=-10.81 \Omega$

$R=|Z|sin \phi = 16 sin 42.5=11.81 \Omega$

$Z=R+jX=(11.81-j10.81) \Omega$

The power factor is $cos \phi =cos 42.5 =0.74$ leading

$X_c= \frac{1}{wc} \implies c= \frac{1}{X_cw}=\frac{1}{10.81*314.6}=0.00029404$

$C= 294.04*10^{-6} F$