A vacuum cleaner is plugged into a 120.0-V socket and uses 2.4 A of current in normal operation when the back emf generated by the electric motor is 98.6 V. Find the coil resistance of the motor.

Answer:

The resistance of the motor is 8.91 ohms.

Explanation:

Given that,

Voltage of the socket, V = 120 V

Current, I = 2.4 A

Back emf generated by the electric motor is, E = 98.6 V

We need to find the coil resistance of the motor. The new emf on the vacuum cleaner is

Answer:The resistance of the motor is 8.91 ohms.

Explanation:Given that,

Voltage of the socket, V = 120 V

Current, I = 2.4 A

Back emf generated by the electric motor is, E = 98.6 V

We need to find the coil resistance of the motor. The new emf on the vacuum cleaner is

[tex]V’=V-E[/tex]

[tex]V’=120\ V-98.6\ V\\\\V’=21.4\ volts[/tex]

The resistance of the motor is given by :

[tex]V’=IR\\\\R=\dfrac{V’}{I}\\\\R=\dfrac{21.4\ V}{2.4\ A}\\\\R= 8.91\ \Omega[/tex]

So, the resistance of the motor is 8.91 ohms. Hence, this is the required solution.