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A 190 mH inductor is connected to an emf given by
v(t) = (161 V) sin(134t).
(a)What is the reactance of the inductor (in Ω)?
(b) Write an expression for the current through the inductor. (Use the following as necessary: t. Assume i(t) is in amps and t is in seconds. Do not include units in your answer.)

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onyebuchinnaji

(a) The reactance of the inductor is 25.46 ohms.

(b) The expression for the current through the inductor is I(t) = (6.32 A) sin(134t)

Ractance of the inductor

The reactance of the inductor is calculated as follows;

XL = ωL

where;

  • ω is angular frequency
  • L is 190 mH

v(t) = (161 V) sin(134t)

v(t) =  V sin(ωt)

The reactance of the inductor is calculated as follows;

XL = (134) x (190 x 10⁻³)

XL = 25.46 ohms

Peak current in the circuit

I₀ = V₀/XL

I₀ = (161) / (25.46)

I₀ = 6.32 A

Expression for the current through the inductor

I(t) = (6.32 A) sin(134t)

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