Question

in an alternating current circuit the phase difference between current i and voltage is phi then wattless component of current will be

Answer 1

The apparent power between v and i is given as,

v*i = vicosФ + jvisinФ

where vicosФ is known as the active power which is responsible for heat produced and visinФ is known as the reactive power or wattless component of v and i which is required to maintain the reactive power consumption in the circuit.

Hence the wattless component is given by visinФ

Answer 2

wattless current is said to be component of that current, which doesn't consume any power in the circuit.

see figure, here phase difference between current and voltage is ϕ ,

then, Icosϕ along the voltage and Isinϕ perpendicular the voltage.

but Isinϕ doesn't produce any power in the circuit because phase angle between $\bf{Isin\phi}$and voltage is π/2.

hence, In an alternating current circuit the phase difference between current i and voltage is phi then $\bf{wattless}$ component of current will be $\bf{Isin\phi}$