Meaning of wattless current

In an AC circuit, the average power consumed is $P = VI\cos\phi$ where:

• $V$ = rms voltage
• $I$ = rms current
• $\phi$ = phase difference between voltage and current

A wattless current means the average power consumed is zero.

So, $P=0 \implies VI\cos\phi = 0$

Since $V$ and $I$ are not zero for a working circuit, we must have $\cos\phi = 0$ $\phi = 90^\circ$

Interpretation of phase difference

A phase difference of $90^\circ$ occurs in a purely reactive circuit, i.e. one having only inductance or only capacitance.

Check the options

A: Purely Resistive circuit
For a pure resistor, $\phi = 0^\circ$, so $P = VI\cos 0 = VI \neq 0$ Hence, not wattless.

B: Purely Inductive circuit
For a pure inductor, current lags voltage by $90^\circ$. $\phi = 90^\circ \Rightarrow \cos\phi = 0$ Therefore, $P=0$ So this is a wattless circuit.

C: LCR series circuit
In general, an LCR series circuit has resistance present, so average power is usually non-zero: $P = VI\cos\phi \neq 0$ unless it is a special ideal case with $R=0$, which is not implied here. So this is not generally wattless.

D: RC series circuit only
An RC series circuit contains a resistor, so average power is consumed in the resistor. Hence it is not wattless.

Conclusion

The circuit is: $\boxed{\text{Purely Inductive circuit}}$

So the correct option is B.