A coil has resistance R=7Ohms and inductance L=1milliHenries and is powered by a

Question

A coil has resistance R=7Ohms and inductance L=1milliHenries and is powered by a generator with variable frequency and maximum voltage V = 10Volts.
(a) At what frequency is the inductive reactance equal to resistance? This is when Z=sqrt(2)*R.
1110 Hz
(b) What is the average power used by the coil when the generator operates at the frequency you found in (a)?
3.57 W
(c) What is the average power used by the coil when the generator operates at 60Hz?
7.12 W
(d) What is the average power used by the coil when the generator operates at one-thousand times the frequency in (a)?
7.14

Explanation / Answer

inductice reactance XL = 2pifL

given this is equal to resistance

so 2pifL = R

f = R/2piL = 7/(2*3.14* 0.001) = 1114.65 Hz or 1.114 KHz

b. at a frequency of 1114.65 Hz

XL =R

thus impedence Z = sqrt(R^2+ Xl^2)

Z = sqrt 2 * R

Z = 1.414* 7   = 9.898 ohms

current i = Vrms/Z = 10/9.898 = 1.01 Amps

so Avg power = Vi = 10 *1.01 = 10.103 Watts

c. when f= 60Hz

Xl = 2pifL = 2*3.14* 60 * 0.001 = 0.3768 ohms

so Z^2 = 7^2 + 0.3768^2

Z =7.01ohms

i = V/Z = 10/7.01

avg power P = Vi/2 = 10/7.01)*10/2 = 7.12 Watts

d. when f = 1114.64 *1000

Xl = 1000* 1114.64*2*3.14* 0.001 = 7000 ohms

Z = 7000

i = 10/7000 = 0.00142 amps

so avg power = Vi /2 = 10* 0.00142*10/2 = 7.14 *10^-3 Watts

e. when f=1/1000 times

avg power = 1000 times of d

P = 7.14 ohms

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