Question

2. Suppose you have a AC motor built from the design below. The square metal wire between the magnets has a side length of.05 magnetic field of magnitude 2 tesla, and that the motor is connected to a 10 ohm resistor via a circuit. meters. Assuming that the permanent magnets create a constant a. If the circuit is connected to an alternating voltage source, then (ignoring the back emf), what will the peak voltage of the voltage source have to be in order to create a peak torque in the motor of 10Nm + O M1T b-The above RL circuit has a 5 ohm resistor and a 2H inductor with a DC battery that supplies 7 volts i. What is the maximum value of the current? ii. How long will it take for the current to reach 2 Ampere?

Answer 1

2 a)

$\tau$ = torque = 10 N m

i = current

B = magnetic field = 2 T

A = area of cross-section = 0.05 x 0.05 = 25 x 10^-4 m²

Torque is given as

$\tau$ = i A B

10 = i (25 x 10^-4) (2)

i = 2000 A

R = resistance = 10 ohm

Peak Voltage is given as

V = i R

V = 2000 x 10

V = 2 x 10⁵ Volts

b)

a)

V = supply Voltage = 7 Volts

R = resistance = 5 ohm

i_p = peak current = V/R = 7/5 = 1.4 A

b)

T = time constant = L/R = 2/5 = 0.4 sec

i(t) = 0.2 A

using the equation

i(t) = i_p (1 - e^-t/T)

0.2 = (1.4) (1 - e^-t/0.4)

t = 0.062 sec