Question

In the circuit shown below, a load having an impedance of 39 + j26 Ω is fed from a voltage source through a line having an impedance of 1 + j4 Ω. The effective, or rms, value of the source voltage is 250 V.

• Calculate the load current IL and load voltage VL.
• Calculate the average and reactive power delivered to the load.
• Calculate the average and reactive power delivered to the line.
• Calculate the average and reactive power supplied by the source

Answer 1

The circuit is a voltage divider with impedances ZL = 39 + j26 Ω and ZT = 1 + j4 Ω.

1- To calculate the load current IL, we can use the voltage divider equation: IL = VL / ZL = VS / (ZL + ZT)

2- To calculate the load voltage VL, we can use the voltage divider equation: VL = IL * ZL

3- To calculate the average power delivered to the load, we can use the formula: Pl = VL * IL * cos(Φ) where Φ is the phase angle between the voltage and current.

4- To calculate the reactive power delivered to the load, we can use the formula: QL = VL * IL * sin(Φ)

5- To calculate the average power delivered to the line, we can use the formula: Pl = VL * IL * cos(Φ)

6- To calculate the reactive power delivered to the line, we can use the formula: QL = VL * IL * sin(Φ)

7- To calculate the average power supplied by the source, we can use the formula: Ps = VS * IL * cos(Φ)

8- To calculate the reactive power supplied by the source, we can use the formula: Qs = VS * IL * sin(Φ)

Note that to calculate the above values, you need to know the values of VS, ZL, and ZT, as well as the phase angle Φ.