a. An air-core coil is connected to a 120 V, 60 Hz source as shown in Fig. 20.42. The current is found to be 5 A, and a wattmeter reading of 75 W is observed. Find the effective resistance and the inductance of the coil. b. A brass core is then inserted in the coil. The ammeter reads 4 A, and the

Question

a. An air-core coil is connected to a 120 V, 60 Hz source as shown in Fig. 20.42. The current is found to be 5 A, and a wattmeter reading of 75 W is observed. Find the effective resistance and the inductance of the coil.
b. A brass core is then inserted in the coil. The ammeter reads 4 A, and the wattmeter 80 W. Calculate the effective resistance of the core.
To what do you attribute the increase in value over that in part (a)?
c. If a solid iron core is inserted in the coil, the current is found to be 2 A, and the wattmeter reads 52 W. Calculate the resistance and the inductance of the coil. Compare these values to those in part (a), and account for the changes.

Accepted Answer

a. [latex]R=\frac{P}{I^2}=\frac{75W}{(5A)^2}=3 \Omega\[0.5cm] Z_T=\frac{E}{I}=\frac{120 V}{5A}=24 Ω\[0.5cm] X_L=\sqrt{Z^{2}_{T}-R^2}=\sqrt{(24 Ω)^2-(3 Ω)^2}=23.81 Ω\[0.5cm] and\hspace{30 pt} X_L = 2\pi fL\[0.5cm] or\hspace{30 pt} L=\frac{X_L}{2\pi f}=\frac{23.81 Ω}{377 rad/s} =63.16 mH [/latex]

b. [latex]R=\frac{P}{I^2}=\frac{80 W}{(4A)^2}=\frac{80 Ω}{16}=5\Omega [/latex]

The brass core has less reluctance than the air core. Therefore, a greater magnetic flux density B will be created in it. Since [latex]P_{eddy}∝f^2B^2, \ and \ P_{hys}∝f^1B^n[/latex], as the flux density increases, the core losses and the effective resistance increase.

c. [latex]R=\frac{P}{I^2}=\frac{52W}{(2A)^2}=\frac{52 Ω}{4}=13\Omega\[0.5cm] Z_T=\frac{E}{I}=\frac{120V}{2A}=60\Omega\[0.5cm] X_L=\sqrt{Z^{2}_{T}-R^2}=\sqrt{(60 Ω)^2-(13 Ω)^2}=58.57 Ω\[0.5cm] L=\frac{X_L}{2\pi f}=\frac{58.57 Ω}{377 rad/s}=155.36 mH [/latex]

The iron core has less reluctance than the air or brass cores. Therefore, a greater magnetic flux density B will be developed in the core. Again, since [latex]P_{eddy}∝f^2B^2, \ and \ P_{hys}∝f^1B^n[/latex], the increased flux density will cause the core losses and the effective resistance to increase.

Since the inductance L is related to the change in flux by the equation L = N(dΦ/di), the inductance will be greater for the iron core because the changing flux linking the core will increase.

Question 20.10: a. An air-core coil is connected to a 120 V, 60 Hz source as...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions