I'm doing AC theory, and I'm looking for different formula to find induced back-EMF. Given inductance, voltage, current, frequency, I'm able to find inductive reactance, current and voltage on each inductor, but I'm really struggling to find something to help me put it together. If anyone has any tips at all they would be greatly appreciated!
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\$\begingroup\$ Show what you have found so far. V = L di/dt pretty much covers all the bases for back-emf in my book. \$\endgroup\$– Andy akaCommented Jun 25, 2014 at 7:13
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\$\begingroup\$ Is there any way I can apply that to an instantaneous value? Are there any other formula you can think of? \$\endgroup\$– Daniel SmithCommented Jun 25, 2014 at 7:15
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\$\begingroup\$ It applies to instantaneous values of V, L and di/dt \$\endgroup\$– Andy akaCommented Jun 25, 2014 at 7:17
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\$\begingroup\$ But how could I relate this to an inductor in a circuit? Without being given any form of time other than my frequency? \$\endgroup\$– Daniel SmithCommented Jun 25, 2014 at 7:20
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\$\begingroup\$ Oh i see, I can translate frequency into Di over dt? \$\endgroup\$– Daniel SmithCommented Jun 25, 2014 at 7:21
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1 Answer
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For an inductor V = \$L\dfrac{di}{dt}\$
This is fundamental and always correct. For instance: -
- If applied voltage is constant at 1V, current ramps linearly from 0 to infinity at a rate of 1/L amps per second. If L is 0.1 henries it ramps at 10 amps per second
- If applied voltage is a 5 Vpk sinewave of 1 radian per second then the differential of current is also a sinewave but with peak value of 5/L
- If the differential of current is a sinewave then current is a cosine wave i.e. it lags the voltage by 90 degrees.
Does this help?
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\$\begingroup\$ I'll have to have more of a look at it when I'm not busy, but I'm sure I can figure out the rest with that, thanks heaps! :) \$\endgroup\$ Commented Jun 25, 2014 at 8:17
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\$\begingroup\$ @Andy aka - shouldn't there be a minus sign in there somewhere? \$\endgroup\$ Commented Jun 25, 2014 at 16:25
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\$\begingroup\$ @jim some say yes some say no. If I connect a 1 henry coil to a 1 volt battery, there is a positive ramping current of 1 amp per sec. If I instantly replace the voltage source with a resistor the voltage reverses. Which should I use therefore. Strictly for induction I should use a neg sign but, for the examples in my answer, I should use positive I reckon. \$\endgroup\$– Andy akaCommented Jun 25, 2014 at 18:22
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\$\begingroup\$ @Andy aka. What does it mean to have 5vpk sinewave of 1 radian per second? Does this mean our frequency is something like 1/2pi? \$\endgroup\$ Commented Jun 26, 2014 at 1:32
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\$\begingroup\$ I used 1 radian per second to make the math easier. 1 rad/sec = 1/2pi Hz as you said \$\endgroup\$– Andy akaCommented Jun 26, 2014 at 7:27