A dc electric motor found in the lab was being examined by a student. It was connected to a power supply and it was not attached to any load.
(a) The student stated, ‘when the motor is switched on, the electrical energy input should cause the motor to start rotating, and the rotation rate should increase without limit since there is no load.’ the validity of this statement, mentioning the principles involved.
(b) Calculate the current flowing in a motor having 210 turns of coil in the armature, which is a 3.0 x 3.0 cm square coil within a magnetic field of 0.023 T, when it is providing a maximum torque of 2.7 x 10-2 Nm.
(c) For the motor used in part (b), calculate the angle the coil is making with the magnetic field when the torque is only one half of its minimum value.
If you were trying "cut and paste" it rarely works here. You will need to type the choices out.
Sra
dfsg
(a) The student's statement is not entirely valid. When a dc electric motor is switched on, the electrical energy input does cause the motor to start rotating. However, the rotation rate does not increase without limit if there is no load. This is because the motor's speed is dependent on the balance between the applied voltage (which creates the electromagnetic field) and the back EMF generated by the rotation of the armature.
The principle involved here is Faraday's law of electromagnetic induction. According to Faraday's law, when the motor starts rotating, the changing magnetic field due to the rotation of the armature induces a back EMF. This back EMF opposes the applied voltage and reduces the net voltage across the motor. As a result, the rotation rate of the motor reaches a stable value where the applied voltage and back EMF are balanced. This stable rotation rate is also known as the no-load speed of the motor.
(b) To calculate the current flowing in the motor, we can use the formula for torque in a dc motor:
Torque = B * I * N * A * sin(θ)
Where:
- Torque (T) is given as 2.7 x 10^-2 Nm.
- B is the magnetic field strength, given as 0.023 T.
- I is the current flowing in the motor (which we need to find).
- N is the number of turns of the coil in the armature, given as 210.
- A is the area of the coil, given as (3.0 cm)^2.
- θ is the angle between the coil and the magnetic field.
Rearranging the formula, we have:
I = T / (B * N * A * sin(θ))
Substituting the given values, we get:
I = (2.7 x 10^-2 Nm) / (0.023 T * 210 turns * (3.0 cm)^2 * sin(θ))
(c) To calculate the angle θ at which the torque is only one half of its minimum value, we first need to find the minimum torque. The minimum torque occurs when the angle between the coil and the magnetic field is 90 degrees, resulting in the maximum sin(θ) value of 1.
Given that the maximum torque is 2.7 x 10^-2 Nm, the minimum torque is half of that:
Minimum torque = (1/2) * 2.7 x 10^-2 Nm = 1.35 x 10^-2 Nm
Now, we can rearrange the torque formula in part (b) to solve for the angle θ:
sin(θ) = T / (B * I * N * A)
Substituting the known values, we get:
1/2 = (1.35 x 10^-2 Nm) / (0.023 T * I * 210 turns * (3.0 cm)^2)
Simplifying the equation and solving for I, we can find the current when the torque is only one half of its minimum value.