Two nodes in a network are connected by a line with an impedance of 0.5 + 1.2j Ω. The voltage at the sending end is 33KV and at the receiving end is 32.5 KV with a lag of 1.5° compared to the sending end..
Calculate the current in the line and the real and reactive power consumed by the line itself.
Standard AC circuit analysis equations.
The Attempt at a Solution
I think I've got this just want to make sure that I'm not doing anything silly with the angles etc:
ISR = VS - VR / 0.5 + j1.2 = (33) - (32.5 ∠ -1.5°) / 0.5 + j1.2
= 763.45 ∠ -8.38°
Real Power consumed = I2*Re(Z) = (763.45)^2 * 1/2 = 291.5 KW
Reactive = I2Im(Z) = (763.45)^2 * 1.2 = 700KVAr
Have I done anything silly? I feel to ask because it seems unusual to me that the reactive power is larger than the real power consumed by the line.
Many thanks !