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## Homework Statement

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.

## Homework Equations

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:

I

_{SR}= V

_{S}- V

_{R}/ 0.5 + j1.2 = (33) - (32.5 ∠ -1.5°) / 0.5 + j1.2

= 763.45 ∠ -8.38°

Real Power consumed = I

^{2}*Re(Z) = (763.45)^2 * 1/2 = 291.5 KW

Reactive = I

^{2}Im(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 !