What will be the phase difference between virtual voltage and virtual current when current in the circuit is wattless (in $^{\circ}$)?

In an $a.c.$ circuit,the voltage applied is $E = E_o \sin \omega t$. The resulting current in the circuit is $I = I_o \sin \left( \omega t - \frac{\pi}{2} \right)$. The power consumption in the circuit is given by:

$A$ lamp consumes only $50\%$ of peak power in an $AC$ circuit. What is the phase difference between the applied voltage and the circuit current?

In an $AC$ circuit,$I = 5 \sin \left( 100t - \frac{\pi}{2} \right)$ and $V = 200 \sin 100t$. The power consumed is

$A$ sinusoidal alternating current of peak value $I_0$ passes through a heater of resistance $R$. What is the mean power output of the heater?

$(a)$ For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.
$(b)$ Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Explain.