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## An ac generator has a frequency of 5.0 kHz and a voltage of 45 V. When an inductor is connected between the terminals of this generator, the

Question

An ac generator has a frequency of 5.0 kHz and a voltage of 45 V. When an inductor is connected between the terminals of this generator, the current in the inductor is 65 mA. What is the inductance of the inductor?

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Physics
3 months
2021-07-21T09:50:58+00:00
2021-07-21T09:50:58+00:00 2 Answers
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## Answers ( )

Answer:

Explanation:

Given that,

Frequency f = 5 kHz = 5000Hz

Voltage V=45V

Current In inductor I = 65mA

I = 65 × 10^-3 = 0.065A

We want to find inductance L

We know that the reactive inductance cam be given as

XL = 2πFL

Where

XL is reactive inductance

F is frequency

L is inductance

Then,

L = XL/2πF

From ohms law

V = IR

We can calculate the receive reactance of the inductor

V = I•XL

Then, XL = V/I

XL = 45/0.065

XL = 692.31 ohms

Then,

L = XL/2πF

L = 692.31/(2π×5000)

L = 0.02204 H

Then, L = 22.04 mH

The inductance of the inductor is 22.04mH

Answer:0.022 HExplanation:From Alternating current,

V = (XL)I………………… Equation 1

Where V = Voltage of the generator, I = current in the inductor, XL = Inductive reactance of the generator.

Make XL the subject of the equation

XL = V/I…………….. Equation 2

Given: V = 45 V, I = 65 mA = 0.065 A

Substitute into equation 2

XL = 45/0.065

XL = 692.31 Ω

But,

XL = 2πFL…………………… Equation 3

Where F = frequency of the generator, L = Inductance of the inductor

Make L the subject of the equation

L = XL/(2πF)……………… Equation 4

Given: F = 5.0 kHz = 5000 Hz, π = 3.14, XL = 692.31 Ω

L = 692.31/(2×3.14×5000)

L = 0.022 H