Question

(a) Find the current through a\(0.500{\rm{ }}H\)inductor connected to a\(60.0{\rm{ }}Hz,{\rm{ }}480{\rm{ }}V\)AC source. (b) What would the current be at\(100{\rm{ }}kHz\)?

Short answer

(a.) The current is obtained as: \(2.55{\rm{ }}A\).

(b.) The current is obtained as: \(1.53{\rm{ }}mA\).

Step-by-step solution

Define Electromagnetic Induction

Magnetic or electromagnetic induction is the process of producing an electromotive force across an electrical conductor in a shifting magnetic field. Michael Faraday discovered induction in\({\rm{1831}}\), which James Clerk Maxwell formally defined as Faraday's law of induction.

Evaluating the formula

The inductive reactance is evaluated using the formula:

\({X_L}{\rm{ }} = {\rm{ }}2\pi fL\)

Knowing the reactance, we then can simply apply the Ohm's law and then write it as:

\(\begin{aligned} I{\rm{ }} &= {\rm{ }}\frac{U}{{{X_L}}}\\ &= {\rm{ }}\frac{U}{{2\pi L}}\frac{1}{f}\end{aligned}\)

Evaluating the current for part a

(a.) The numerical value in the first case will be:

\(\begin{aligned} I{\rm{ }} &= {\rm{ }}\frac{{480}}{{2\pi {\rm{ }} \times {\rm{ }}0.5}} \times \frac{1}{{60}}\\ &= {\rm{ }}2.55{\rm{ }}A\end{aligned}\)

Therefore, the current is: \(2.55{\rm{ }}A\).

Evaluating the current for part b

(b.) The numerical value in the second case will be:

\(\begin{aligned} I{\rm{ }} &= {\rm{ }}\frac{{480}}{{2\pi {\rm{ }} \times {\rm{ }}0.5}} \times \frac{1}{{1{\rm{ }} \times {\rm{ }}{{10}^5}}}\\ &= {\rm{ }}1.53{\rm{ }}mA\end{aligned}\)

Therefore, the current is: \(1.53{\rm{ }}mA\).