Given data:-

Parallel connected R-L load

Supply voltage, $V=200\ Volts$

Supply frequency,$f=50Hz$

Resistance of circuit, $R=10\Omega$

Inductance of the circuit, $L=31.8mH = 0.0318\ Henery$

As inductive reactance of the circuit is given by, $X_L=\omega L=2\pi fL$

$\therefore X_L=2\pi fL=2\pi\times 50\times 0.0318=9.99\Omega\approx10\Omega$

Lets consider Parallel connected R-L circuit shown in figure below-

(i) Current through resistive branch:-

$I=\dfrac{V}{R}=\dfrac{200}{10}=20\ A$

Current in resistive branch is in phase of voltage.

(ii) Current through pure inductive branch:-

$I_L=\dfrac{V}{X_L}=\dfrac{200}{10}=20\ A$

Current through pure inductor lags the voltage by 900.

Lets consider the voltage & current phasor for given circuit as shown in figure below-

(ii) Total resultant current:-

From above phasor, total current, $I=\sqrt{I_R^2+I_L^2}=\sqrt{10^2+10^2}=10\sqrt2\ A$

(iv) Power factor:-

Power factor angle, $\phi = \tan^{-1}\dfrac{X_L}{R}= \tan^{-1}\dfrac{10}{10}=45^0$

As power factor of a load is given, $\cos\phi$

$\therefore load\ power\ factor, \cos\phi=\cos45=0.71 \ lagging$