Question

An alternator has a synchronous reactance of 20% and negligible resistance. Its voltage regulation when working on full load at 0.8 pf lag will be _________%

• A. 13

Answer 1

The correct option is A 13
$E_f^2=(V_{t}cos\varphi {)}^2+(V_{t}sin\varphi +I_a{X}_s{)}^2$

$E_f^2=V_t^2[{0.8}^2+{(0.6+\frac{I_a{X}_s}{V_t})}^2]$

$E_f^2=V_t^2[{0.8}^2+(0.6+0.2{)}^2]$

$E_f=1.13V_t$

$\text{Voltage regulation}=\frac{E_f-V_t}{V_t}\times 100\%$

$=\frac{1.13V_t-V_t}{V_t}\times 100\%=13\%$