Inductive reactance and length of the solenoid

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SUMMARY

The discussion focuses on calculating the inductive reactance and length of a solenoid used as an inductor in a circuit. Given a solenoid with a radius of 8.0 x 10-3 m and 170 turns/cm, connected to a 15 V rms source at 22 kHz, the inductive reactance (XL) can be calculated using the formula XL = 2πfL. The self-inductance (L) is derived from the equation L = μn2πr2l, where μ is the permeability of free space. The user successfully resolved the calculations independently.

PREREQUISITES
  • Understanding of inductive reactance and its formula (XL = 2πfL)
  • Knowledge of solenoid parameters including radius, turns per unit length, and self-inductance
  • Familiarity with the concept of rms voltage and current
  • Basic grasp of electromagnetic theory and relevant equations
NEXT STEPS
  • Study the derivation of the inductive reactance formula (XL = 2πfL)
  • Explore the properties of solenoids and their applications in circuits
  • Learn about the permeability of free space (μ) and its significance in inductance calculations
  • Investigate the effects of frequency on inductive reactance in AC circuits
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Students and professionals in physics and electrical engineering, particularly those focusing on circuit analysis and electromagnetic theory.

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Homework Statement


A solenoid with a radius of 8.0 10-3 m and 170 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of 15 V rms at 22 kHz, an rms current of 3.7 10-2 A is measured. Assume the resistance of the solenoid is negligible.
(a) What is the inductive reactance?
(b) What is the length of the solenoid?

r = 8E-3 m
n = 170E2 turns/m
Vrms = 15 V
f = 22E3 Hz
Irms = 3.7E-2 A
Area = pir^2 = 2.01E-4 m^2

Homework Equations


XL = 2pifL

L = μn^2pir^2l

The Attempt at a Solution


I know how to utilize the equations, but my problem is finding L (self-inductance) in order to solve both part a and b. I try looking throughout my physics book, but nothing.

a) XL = 2*pi*22E3*L

b) L = 4piE-7*17000^2*3.14*8E-3*l
 
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Nevermind, I managed to figure the problem out myself.
 

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