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I'm studying for an exam, and have come across a question I don't. really understand

The question gives us a back-emf constant and asks for a rated back-emf. Now I know that the back-emf constant is k, but the rated back-emf confused me at first. When the lecture went through the questions, what he said confused me.

The lecturer says that the rated back-emf is E? I don't understand how the back-emf can be both E and k at the same time. What exactly is the difference between E and k? I think the main question I am asking is what exactly is this question asking me to do?

Here is the question:

A DC machine has a back-emf constant of 0.24 V/(rad/s) and a resistance of 0.5 ohms. It is operating from a 12V DC power supply. At its rated speed of 400 rpm, calculate its rated back-emf (that is, the back-emf at rated speed).

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  • \$\begingroup\$ Hint. What are the units of k? What are the units of E? What is the dimensional difference between them? \$\endgroup\$
    – user16324
    Commented Jun 18, 2015 at 12:14
  • \$\begingroup\$ @BrianDrummond I know that E is volts and k is volts/rad/second, but why are both of them called "back-emf"? what's the relationship there? \$\endgroup\$
    – Vaderico
    Commented Jun 18, 2015 at 13:09
  • \$\begingroup\$ Convert rpm into rad/s ... \$\endgroup\$
    – Chu
    Commented Jun 18, 2015 at 13:40
  • \$\begingroup\$ One of them isn't called back-emf, because it isn't an EMF. It's a constant relating EMF to speed. The dimensional difference between them : speed: is the relationship. \$\endgroup\$
    – user16324
    Commented Jun 18, 2015 at 14:32

2 Answers 2

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There are two key constants with respect to electrical machines

1) \$K_e\$ The BackEMF constant. Units in Volts/rpm (volts/rads ...) -> what voltage will be generated at the terminals if the rotor is spinning.

2) \$K_t\$ The Torque constant. Units in Nm/A - What torque will be generated if current is injected into the stator

(there is a 3rd... \$K_v\$, velocity constant, the reciprocal of \$K_e\$, rpm/Volts) - what speed the rotor could spin at for a given applied voltage

In theory \$K_t\$ = \$K_e\$. In practice, \$K_t\$ < \$K_e\$ as \$K_t\$ is taken at rated current & corresponds to Iron saturation.

So the question:

A DC machine has a back-emf constant of 0.24 V/(rad/s) and a resistance of 0.5 ohms. It is operating from a 12V DC power supply. At its rated speed of 400 rpm, calculate its rated back-emf (that is, the back-emf at rated speed).

We thus know \$K_e\$ = 0.24V/rad/s

We also know the rpm = 400rpm

convert rpm to rad/s: \$ \omega = \frac{rpm * 2 * \pi}{60} = 41.8879rad/s \$

There is one more step to get the rated terminal voltage, but I will leave that

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I think you are overthinking this.

The back-emf constant is a property of a machine that tells you how the generated EMF relates to rotor speed.

The back-emf of an actual running machine is the generated EMF in that machine.

The rated back-emf would then just be the actual EMF generated at the machine's rated speed.

I don't know if I can say too much more without giving you the answer to your homework.

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