Question

You want the current amplitude through a 0.450 mH inductor (part of the circuitry for a radio receiver) to be 1.50 mA when a sinusoidal voltage with an amplitude of 13.0 V is applied across the inductor. What frequency is required?

Answer 1

3.067MHz

Step-by-step explanation:

The formula for calculating the voltage across an inductor is expressed as

`V_l = IX_l\\\\Since\ X_l = 2\pi fL\\V_l = I(2\pi fL)`

Given parameters

current amplitude I = 1.50mA = 1.5*10⁻³A

inductance L = 0.450mH = 0.450*10⁻³H

Voltage across the inductor
`V_l` = 13.0V

Required

frequency f

Substituting the given parametres into the formula, we have;

`V_l = I(2\pi fL)\\\\13 = 1.50*10^(-3)(2*3.14*f*0.450*10^(-3))\\\\13 = 4.239*10^(-6)f\\\\f = (13)/(4.239*10^(-6)) \\\\f = 3,066,761 Hertz\\\\f = 3.067MHz`

Hence, the frequency required is 3.067MHz