Solve DC Motor Problem: 250W 24V 1800rpm

[TheRedDevil18]

Homework Statement

A 250W 24V 1800rpm DC machine is operated as a shunt connected motor and connected to a fan that draws 60% full load current through the armature.

1) Sketch the circuit

2) The field winding requires a current of 0.8A to produce a motor EMF of 24V. Determine the field resistance required to produce the field current if the armature resistance is 0.1 ohms.

3) Determine the input voltage and current required

4) Determine the efficiency if the rotational losses are 15W

Homework Equations

The Attempt at a Solution

Heres my sketch, hope it's clear

2) If the field current is 0.8A since that's the current that flows through the windings, then the field resistance would be Rf = E/IF = 24/0.8 = 30 ohms, Is that correct ? or does it depend on the terminal voltage ?

3) By input voltage they mean terminal voltage, right ?, so the terminal voltage has to be slightly higher than the machines rated voltage in order to account for losses ?, so

First, armature current
Ia = Rated Power/Rated Voltage = 250/24 = 10.42A

So It(Terminal Current) = Ia+If
= 10.42+0.8 (Field Current)
= 11.22A

Vt (Terminal Voltage) = E + Ia*Ra
= 24 + (10.42)(0.1)
= 25.04V

4) Input Power = Vt*It
= 25.04*11.22
= 280.95 W

They said the load draws 60% of the full load current, so
0.6*10.42
= 6.25A

I'm not sure if it will be 60% of the rated voltage also, will it ?, I did it in my calculation
0.6*24 = 14.4V

Pout = Pmech - Plosses
= (14.4)(6.25) - (6.25)²(0.1) This is the armature loss - 15 (Rotational loss)
= 71.09 W

So, efficiency = Pout/Pin
= 0.25*100
= 25%

 

[KataKoniK]

Hi there,

Thank you for your post and for showing your attempt at the solution. Your sketch looks clear and accurate.

For part 2, you are correct that the field resistance would be Rf = E/IF = 24/0.8 = 30 ohms. This calculation is independent of the terminal voltage, as it is based on the desired field current and the motor EMF.

For part 3, you are correct that by input voltage, they mean the terminal voltage. However, your calculation for the terminal voltage is incorrect. The terminal voltage should be equal to the motor EMF, which is 24V, since there is no external resistance in the circuit. So, the terminal current would be 10.42A + 0.8A = 11.22A, and the terminal voltage would be 24V.

For part 4, your calculation of the input power is correct. However, for the output power, it should be Pout = Pmech - Plosses = (14.4)(6.25) - (6.25)^2(0.1) - 15 = 71.09W. This includes the armature losses, rotational losses, and the losses in the circuit. So the efficiency would be 71.09/280.95 = 25.33%.

Overall, your calculations are mostly correct, but there are some minor errors in the values used. Good job on showing your work and attempting the solution!