Question

A balanced three-phase, star-connected load of 100 kW takes a leading current of 80 A, when connected across a 3-phase 1100 V, 50 Hz supply. The capacitance of the load per phase is

• A. $531.4\mu F$
• B. $5.99\mu F$
• C. $7.49\mu F$
• D. $5.21\mu F$

Answer 1

The correct option is A $531.4\mu F$

Here, Line voltage, $V_L=1100V$
Line current, $I_L=80A$
Power supplied, $P=100kW$
$\therefore$ power factor of the circuit,
$\cos \varphi =\frac{P}{3V_L{I}_L}$
$=\frac{100\times {10}^3}{\sqrt{3}\times 1100\times 80}=0.656$ leading
Impedance of the load per phase,
$Z=\frac{V_{ph}}{I_{p}h}=\frac{\frac{V_L}{\sqrt{3}}}{I_1}$
$=\frac{\frac{1100}{\sqrt{3}}}{80}=7.94\Omega$
Resistance of the load per phase,
$R=Z\cos \varphi =7.94\times 0.656$
$=5.208\Omega =5.21\Omega$
Reactance of the load per phase,
$X_C=\sqrt{Z^2-R^2}$
$=\sqrt{(7.94{)}^2-(5.21{)}^2}=5.99\Omega$
Capacitance of the load per phase,
$C=\frac{1}{2\pi f{X}_C}$
$\frac{1}{2\pi \times 50\times 5.99}=531.4\mu F$