# RL-circuit & power/transformer

1. Mar 16, 2009

### Hannisch

Okay, I've got two problems that are giving me issues and it's quite annoying. We're all kinda stuck on them and we couldn't get our teacher to explain them to us (yarghhh).

1. The problem statement, all variables and given/known data
A motor is designed to operate on 117 V and draws a current of 12.2 A when it firsts starts up. At its normal operating speed, the motor draws a current of 2.30 A. Obtain (a) the resistance of the armature coil, (b) the back emf developed att normal speed and (c) the current drawn by the motor at one-third normal speed.

2. Relevant equations
$$I(t) = \frac{E}{R}(1-e^{-{\frac{R}{L}t}})$$
$$E= - N \frac{d \Phi }{dt} = -L \frac{dI}{dt}$$

Where E = emf.

3. The attempt at a solution
So, what we at first thought for (a) was that normal speed is some sort of .. evening out or something similar to that, so we wanted to use Ohm's law to find the resistance (now looking at the numbers that's sort of absurd - how can Imax be lower than the initial one? Doesn't really make sense), but obviously that's wrong, we realised when we came to (b). And we're stuck. We don't know how to proceed and for me it's a bit what's what? Is 12.2 the Imax? Like, what does the question actually say?

1. The problem statement, all variables and given/known data
A generating station is producing 1.2 * 106 W of power that is to be sent to a small town located 7 km away. Each of the two wires that compromise the transmission line has a resistance per kilometre of length of 5.0 * 10-2 Ohm/km. (a) Find the power used to heat the wires if the power is to be transmitted at 1200 V. (b) A 100: l [okay, so I'm not too sure about this last thing - it looks like it says this, but I can't be 100% sure, bad copy..] step-up transformer is used to raise the voltage before the power is transmitted. How much power is now used to heat the wires?

2. Relevant equations

3. The attempt at a solution
I need conceptual help here, first of all - this question is not from our textbook, but another one which my teacher has and our book apparently doesn't go through this enough, cos I'm so lost. I don't even really know which angle to approach the problem from. Hint in the right direction, anyone?

2. Mar 16, 2009

### rrogers

Your working too hard at it. Replace the motor with a series RC and take startup as Vc=0,
Then compute the resistance. having the resistance, and subsequent applied voltage and current you can calculate Vc. Subsequently 1/3 speed will produce Vc/3 etc...
The RC network is just an intellectual prop and can dropped in favour of straightforward calculations.
Ray

3. Mar 16, 2009

### Hannisch

Ah, thanks so much! I wasn't even close to thinking RC - we haven't done them in a while and I apparently just thought that since we're currently doing magnetic flux and inductance it would have something to do with that.

4. Mar 16, 2009

### rrogers

Well in my experience the RC model is most intuitve to start; and then add the L when dealing with switching transients.
This is experience, but really should write out the dynamic differential equation for the current loop and then make identifications of terms with RLC for a intuitive representation. Writing the loop equations correctly in the time domain will allow you to deal with more complicated problems. For instance the windings have interwinding capacitance that bypasses the L and you could also loads that have complex dynamics that need to be incorporated. Hopefully these are all refinements of a simple start, but sometimes are not. KISS but only simple enough to capture the problems.
Of course the more correct way is to directly transform the "real" dynamic equations into the LaPlace domain and manipulate; but if you only deal with motors once every decade then the RLC model is handy.
Ray