Question

What is the reactance in Ohms of a $2.00\,\,H$ inductor at a frequency of $50.0\,\,Hz$ ?

Answer 1

Learn the formula for calculating the reactance of an inductor. The formula for calculating the inductive reactance of a coil is that the inductive reactance is the product of $2$ times $\pi$ ,the frequency of the ac current, and the inductance of the coil.

Formula Used:
$\boxed{{X_L} = \omega L}$
Where, ${{\text{X}}_{\text{L}}}{\text{ = }}\,$Inductive Reactance ${\text{\omega = }}$angular Frequency, ${\text{L = }}$ Inductance.
Here,
$\omega = 2\pi f$
Where, $f =$ Frequency.

Complete step by step answer:
As per the given problem, given values are as follow
$L = 2.00\,H$
The SI unit of the inductor is Henry.
$f = \,50.0Hz$
The SI unit of frequency is Hertz.Applying the above formula of Inductive reactance we get,
$\left( \Omega \right){X_L} = \omega L$
Where, $\omega = 2\pi f$
By putting $\omega$ value in the above inductive reactance formula we get,
${X_L} = 2\pi f\,L$

Putting the given value with proper SI unit we get,
${X_L} = 2\pi \times 50.0Hz \times 2.00H$
By putting $\pi = 3.14$ in the above reactance we get,
${X_L} = 2 \times 3.14 \times 50.0Hz \times 2.00H$
$\Rightarrow {X_L} = 3.14 \times 2 \times 100\,\,\Omega$
$\Rightarrow {X_L} = 6.28 \times 100\,\,\Omega$
$\therefore {X_L} = 628\,\Omega$
SI unit of inductive reactance is Ohm $\left( \Omega \right)$ .

Therefore the correct answer to this problem is $628\Omega$.

Note: An inductor is a passive two terminal electronic component that stores energy in a magnetic field when electric current flows through it. It typically consists of an insulated wire wound into a coil.Inductor is a component that allows DC, but not AC, to flow through it. It is also referred to as coil or choke.In Inductor, voltage leads current by $90$ degree.