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I've heard that resistors are used to decrease current to a particular appliance, such as in the regulator of a fan. However, I've also heard that the total current in a circuit is always the same- in other words, all the current leaving the positive terminal of the battery reaches as it is to the negative terminal. How can this be? The two statements are contrary. How can the total current be the same if a resistor is reducing current at some point in the circuit?

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Think of a chain driving a bicycle wheel. If you slow down the wheel by rubbing it against your hand, does only part of the chain slow down? No, every point in the chain has to always travel at the same speed, so the entire chain slows down, transferring the slowness back to the pedals and making them harder to turn. Using the current in a wire to transfer energy from a generator to a load (or using the water current in pipes) works the same way. –  endolith May 11 '13 at 16:50
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3 Answers

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Regarding what you consider to be a contradiction:

How can the total current be the same if a resistor is reducing current at some point in the circuit?

The current at any point in the circuit is the same because the current distribution in the circuit has reached a steady state (i.e., charge buildup is forbidden). Your intuition is telling you that the presence of resistance means the motion of the electrons is "damped" and that therefore some current must be, in some sense, "lost". The basic sense you have of this is right, but this "loss of current" is balanced by the driving force (the battery).

Regarding your first statement:

I've heard that resistors are used to decrease current to a particular appliance, such as in the regulator of a fan.

To be clear, adding a resistor to the circuit does reduce the current that flows through the entire circuit (as compared to the circuit without the resistor). However, the current at two points in the circuit is still the same.

Note: It should be understood, as implied by your question, that we're discussing a simple one-loop circuit. The notions mentioned above apply to more complex circuits, but would need to be generalized a little.

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In a way you could see it as a waterpipe that narrows down half way. Eventough the first half of the pipe is able to transport more water, the amount of water that comes out is still the same as what u pump in. –  user17615 Mar 21 '13 at 15:09
    
Oh I see. However, according to Larry's answer, part of the current flowing through a resistor is converted to heat energy- thereby reducing the outflow of current. In this case shouldn't there be greater current before the resistor than after it? How come all the current in the circuit goes down? –  Ghost Mar 22 '13 at 4:45
    
@Ghost The current is greater before the resistor is added to the circuit. But the resistor does not induce spatial variations in current after it has been added. There is no way the current can vary spatially (be different at different locations) if you require a steady state (no buildup of charge) together with charge conservation. Similarly, in Michiel's example, water is conserved and does not build up anywhere. –  Joshua Barr Mar 22 '13 at 8:20
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We know we can't change the mains supply voltage or fan's coil's resistance itself to control speed(via current) so we place a $external\space resistance$ in series with fan.This drops voltage across fan by some amount and $V(across\space fan)=I\times R(fan)$ gives the changed current in fan.

$V(across\space fan) = \frac {R(fan)\times V(mains)}{R(fan)+R(ext.)}$

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The atoms in a resistor scatter and absorb the energy from the charge carriers in the current. So some of the average kinetic energy of the current is converted to heat in the resistor, and the current is reduced, compared to if the resistance wasn't there.

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protected by Qmechanic Apr 2 at 21:34

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