Answer :

Option (a):

Let us try to find out the average current. The current is given by:

Where I_{0} is the maximum current, ω is the angular frequency (2π times frequency) and ϕ is the phase angle. The average current is:

As I_{0} is constant,

The average of any sinusoidal function over an interval of multiple of 2π is zero. We take the average current over an interval of 2π (the whole period). Hence, the average is zero. Thus, (a) is correct.

Option(b):

As voltage varies sinusoidal, its average is zero. It is similar to what we have done in option(c). The rms voltage is 220V not the average voltage. Hence, (b) is wrong.

Option(c):

We have can have an arbitrary mix of resistors, capacitors and inductors in household circuits. In fact, the phase difference of 90^{°} is only in case the circuit is purely capacitive or inductive. It is not the case with the powers supply coming to our house. Hence, (c) is wrong.

Option (d):

Note that

Both of these quantities are always positive. Hence, cos(ϕ) is always positive. This is possible in only first and fourth coordinate. Hence, . Hence, .

Thus, (d) is correct.

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