Calculating Field Current and Resistance for a DC Motor

[Vagrant]

Homework Statement

A dc machine(6W, 120V,1500rpm) is separately excited and delivers rated current at rated terminal voltage.Field winding is connected to 120V supply. R_fw=100$$\Omega$$.
a) Determine the value of field current
b) Determine the value of R_fc required.

Homework Equations

V_f= I_fR_f

The Attempt at a Solution

In the question the value of V_f is given, while both I_f and R_f are variables. So I need another relation to find out both the values. Is there another relation that I'm missing?

 

[montoyas7940]

Unless I misunderstand the problem, you can get everything you need from the power equations P=IE and P=I^2*R.

 

[piercas]

Yes, there is another relation that can help you solve for both If and Rfc. The equation for calculating the resistance of a DC motor is:

Rm = (Vt - (If * Rf)) / Ia

Where:
Rm = total resistance of the motor
Vt = terminal voltage
If = field current
Rf = field winding resistance
Ia = armature current

Since the motor is delivering rated current at rated terminal voltage, we can substitute these values in the equation:

Rm = (120V - (If * 100Ω)) / 6W

We also know that the rated speed of the motor is 1500rpm, which can be converted to revolutions per second (rps) by dividing by 60:

rps = 1500rpm / 60 = 25rps

We can then use the equation for calculating the back emf of a DC motor:

Eb = (Vt - (Ia * Ra)) / rps

Where:
Eb = back emf
Ra = armature resistance

Again, substituting the known values:

Eb = (120V - (6W * Ra)) / 25rps

Since the motor is delivering rated current, we can equate the back emf to the terminal voltage:

Eb = Vt

Which gives us:

Vt = (120V - (6W * Ra)) / 25rps

Now, we can solve for Ra:

Ra = (120V - (Vt * 25rps)) / 6W

Substituting this value for Ra into the first equation, we get:

Rm = (120V - (If * 100Ω)) / 6W

Simplifying:

Rm = (20V - If * 100Ω) / W

Now, we can substitute this value for Rm into the equation:

Rm = (20V - If * 100Ω) / W

And solve for If:

If = (20V - Rm * W) / 100Ω

Since we know the total resistance of the motor, we can plug in that value for Rm and solve for If:

If = (20V - 6W * W) / 100Ω = 0.14A

Now that we have the value for If, we can use the equation for calculating field current