Calculating Armature Torque for 250V DC Motor

[Reefy]

Homework Statement

A 250V shunt dc motor runs at 1000rpm while taking a current of 25 A. The motor has armature and field resistance as 0.2W and 250W respectively. Calculate

(a) The speed when the load current is 50A.

(b) Armature torque developed at both speeds.

Homework Equations

I_L = I_a + I_sh

V_t = I_shR_sh = E_a + I_aR_a

P_output = Tω = T(2πN)

The Attempt at a Solution

I already solved part a and got N₂ = 979.6 rpm

I actually just have a question of solving part B. How exactly do I compute the output without the torque and angular speed.

Is P_output = I_aR_a

or P_output = I_aR_a - (Iron + Friction) losses

 

[cnh1995]

field resistance as 0.2W**Ω** and 250W**Ω**

The speed when the load current is 50A.

Is it the armature current or the total current supplied by the supply?

Armature torque developed at both speeds.

This means you need to find the mechanical power developed in the motor. Do you know the relation between back emf and mechanical power developed?

 

[Reefy]

I don't know why it says W. It is ohms.

The load current is the current supplied by V_t.

 

[Reefy]

P_input(1) = V_tI_L1 = (250 V)(25 A) = 6250 A at the first speed

and it is P_input(2) = V_tI_L2 = (250 V)(50 A) = 12500 A at the 2nd speed

 

[cnh1995]

P_input(1) = V_tI_L1 = (250 V)(25 A) = 6250 A at the first speed

and it is P_input(2) = V_tI_L2 = (250 V)(50 A) = 12500 A at the 2nd speed

Ok.
You need to find the armature current first. You know the total current and field resistance. How would you calculate the armature current?

 

[Reefy]

I_a1 = I_L1 - I_sh = 25A - 1A = 24A

I_a2 = I_L2 - I_sh = 50A - 1A = 49A

 

[cnh1995]

I_a1 = I_L1 - I_sh = 25A - 1A = 24A

I_a2 = I_L2 - I_sh = 50A - 1A = 49A

Correct.
You can calculate back emf from this. What is the equation describing the relation between back emf and mechanical power developed? Back emf is the electrical feedback of mechanical energy developed.

 

[Reefy]

Correct.
You can calculate back emf from this. What is the equation describing the relation between back emf and mechanical power developed? Back emf is the electrical feedback of mechanical energy developed.

That's what I'm unsure of. I know that P_input - P_output = the total losses (Copper, iron, friction).
And Copper Loss is I²_aR_a + I²_shR_sh

 

[cnh1995]

That's what I'm unsure of. I know that P_input - P_output = the total losses (Copper, iron, friction).
And Copper Loss is I²_aR_a + I²_shR_sh

Those are all electrical powers. The relation between back emf and mechanical power is P_m=E_bI_armature. Can you proceed from here?

 

[Reefy]

Ooohh. Yeah, its the conceptual idea I don't get. I don't get why we have to use mechanical power instead of electrical

 

[cnh1995]

Ooohh. Yeah, its the conceptual idea I don't get. I don't get why we have to use mechanical power instead of electrical

You are asked to find the torque and speed. These are associated with mechanical power. Now, how do you write mechanical power in terms of torque and speed?

 

[Reefy]

You are asked to find the torque and speed. These are associated with mechanical power. Now, how do you write mechanical power in terms of torque and speed?

T = P_M/ω = E_aI_a/(2πN)

 

[cnh1995]

T = P_M/ω = E_aI_a/(2πN)

Right.

 

[Reefy]

Thanks, I see the mistake I was making! It was pretty simple, I must be tired. Appreciate the help again