Answer:
V(t) = XLI₀sin(π/2 - ωt)
Explanation:
According to Maxwell's equation which is expressed as;
V(t) = dФ/dt ........(1)
Magnetic flux Ф can also be expressed as;
Ф = LI(t)
Where
L = inductance of the inductor
I = current in Ampere
We can therefore Express Maxwell equation as:
V(t) = dLI(t)/dt ....... (2)
Since the inductance is constant then voltage remains
V(t) = LdI(t)/dt
In an AC circuit, the current is time varying and it is given in the form of
I(t) = I₀sin(ωt)
Substitutes the current I(t) into equation (2)
Then the voltage across inductor will be expressed as
V(t) = Ld(I₀sin(ωt))/dt
V(t) = LI₀ωcos(ωt)
Where cos(ωt) = sin(π/2 - ωt)
Then
V(t) = ωLI₀sin(π/2 - ωt) .....(3)
Because the voltage and current are out of phase with the phase difference of π/2 or 90°
The inductive reactance XL = ωL
Substitute ωL for XL in equation (3)
Therefore, the voltage across inductor is can be expressed as;
V(t) = XLI₀sin(π/2 - ωt)
