Discussion
In the case of series compensation, if 75% of the compensation is used, the maximum power transferred will ______.
Answer: C
The maximum power that a line can transfer is inversely proportional to its reactance. A series capacitor reduces the net reactance, and with a degree of compensation \(k\)
\[ \begin{aligned} X_{net} \\ &= X(1 - k),\qquad P_{max} \propto \frac{1}{X(1 - k)} \end{aligned} \]
For 75 per cent compensation, \(k = 0.75\):
\[ \frac{P'_{max}}{P_{max}} = \frac{1}{1 - 0.75} = 4 \]
So the maximum power transferred becomes four times the original. The power would be doubled at 50% compensation. The answer is option C.
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