Question

A series R L circuit is connected to a 110V, 50 Hz ac source. If the voltage across the resistor is 85 V, 

find the power dissipated in the circuit, if the value of inductor is 0.05 H

Answer 1

Let us introduce the notation

$U=110 V,f=50 Hz, U_R=85 V, L=0.05H$

1).Determine the resistance of the inductor

$X_L=2 \cdot \pi \cdot f \cdot L=2 \cdot 3.14 \cdot 50 \cdot 0.05=15.71 \Omega$

2).Determine the voltage across the inductor

$U_L=\sqrt{U^2-U_R^{2}}=\sqrt{110^2-85^{2}}=\sqrt{12100-7225}=69.82V$

3).Determine the current in the circuit

$I=\frac{U_L}{X_L}=\frac{69.82}{15.71}=4.45A$

4).Determine the total power of the circuit

$S=U \cdot I=110 \cdot4.45=489.5VA$

5).Determine the reactive power of the circuit

$Q=I^2 \cdot X_L=4.45^2 \cdot 15.71=311.1var$

5).Determine the active power dissipated in the circuit

$P=\sqrt{S^2-Q^{2}}=\sqrt{489.5^2-311.1^{2}}=377.93W$