An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi/4`. If element X is a pure resistor of 100 Ω,

**(a)** name the circuit element Y.

**(b)** calculate the rms value of current, if rms of voltage is 141 V.

**(c) **what will happen if the ac source is replaced by a dc source

#### Solution

**(a) **We have,

Φ = π/4

tan Φ = 1

`tanphi = "Reactance"/"Resistance"`

Reactance = Resistance

Y = 100 Ω

As, ϕ > 0°, means voltage ahead of current Hence element Y is an Inductor.

**(b)**

`"R.m.s value of current" = "R.m.s value of voltage"/"Impedance"`

`"i"_"Rms" = 141/sqrt((100)^2+ (100)^2)`

`"i"_"Rms" = 141/(100sqrt2) = 141/(100 xx 1.41)`

i_{Rms} = 1 A

**(c) **If the Ac is Replace by DC, then the Inductor will behave as a short circuit, and the circuit will be purely Resistive.