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Chapter 31: Q86P (page 903)

When under load and operating at an rms voltage of 220V, a certain electric motor draws an rms current of 3.00A. It has a resistance of 24.0Ωand no capacitive reactance. What is its inductive reactance?

Short Answer

Expert verified

The inductive reactance is 69.3Ω.

Step by step solution

01

Step 1: Given

  1. The rms voltage, Vrms=220V.
  2. The rms current, Irms=3.00A.
  3. Resistance, R=24.0Ω.
02

Determining the concept

By using the values of rms voltage and rms current, find the impedance of the circuit and by using the value of impedance, find the inductive reactance.

The formula are as follows:

  1. Impedance,Z=VrmsIrms.
  2. Impedance, Z2=R2+XL2.
03

Determining the inductive reactance 

The impedance is given by,

Z=VrmsIrms,Z=2203,Z=73.33Ω

Now, use this impedance and the given value of resistance to find the inductive reactance.

Z2=R2+XL2XL2=Z2-R2XL2=73.332-242XL=69.3Ω

Hence, the inductive reactance is 69.3Ω.

By using the values of rms current, rms voltage, and resistance, found inductive reactance.

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