Honestly, this is a homework question. A screenshot of it is given below:

Variable Voltage Divider

Okay these are the things I have done in order to take the answer.

  1. First I calculate the equivalent resistance which comes form 1000 ohms and 10 ohms.
  2. Therefore I assume that total resistance of the circuit is increasing.
  3. And since the potential difference is constant for the equivalent resistance, I get the relationship of current is indirectly proportional to resistance by using Ohm's law.

So according to my argument a graph should indicate a decrement of current with distance PQ, but here in the answer I don't have such a thing. So I think I have done something wrong, so that is why I'm asking this question here!

  • \$\begingroup\$ If you move X upwards, I'd say the QX decreases (resistance is directly proportional to length).This will come in series with a parallel combo of XP and 10 ohm. Tip : You can find this equivalent resistance ( Qx + ( Px || 10) ) and differentiate it to check the slope. \$\endgroup\$ – Plutonium smuggler May 14 '15 at 10:43
  • \$\begingroup\$ Your pathway seems a longcourse \$\endgroup\$ – On the way to success May 14 '15 at 11:05
  • \$\begingroup\$ Its a path to sucess !! :P \$\endgroup\$ – Plutonium smuggler May 14 '15 at 11:06
  • \$\begingroup\$ Try a couple of examples: What is the current when X=P? What is it when X=Q? What is it when X is halfway between P and Q? You'll eventually see a pattern that resembles one of the graphs. \$\endgroup\$ – Dave Tweed May 14 '15 at 11:17
  • \$\begingroup\$ could you say the which path that the current will take when X=P \$\endgroup\$ – On the way to success May 14 '15 at 11:21

When the wiper is at P the resistance is (0Ω || 10Ω) + 1000Ω = 1000Ω. At Q it is 1000Ω || 10Ω ~= 10Ω. Therefore the resistance decreases as the wiper moves from P to Q, and subsequently the current increases. Therefore all graphs are potentially correct.

In order to determine which of the graphs is correct, write out the equation for the current in terms of the resistance and wiper position and plot it.

  • \$\begingroup\$ How can you say "the wiper is at P the resistance is (0Ω || 10Ω) + 1000Ω = 1000Ω. At Q it is 1000Ω || 10Ω ~= 10Ω." Note:I get the calculation you have done but how do you take that, I mean what is theory behind that? \$\endgroup\$ – On the way to success May 14 '15 at 15:48
  • \$\begingroup\$ That's how a potentiometer is constructed; part of the resistance is between one terminal and the wiper, and the rest is between the wiper and the other terminal. When the wiper is all the way at each end the resistance to the closest terminal is (nominally) 0Ω, and the resistance to the further terminal is the full rating. \$\endgroup\$ – Ignacio Vazquez-Abrams May 14 '15 at 15:51
  • \$\begingroup\$ Okay, when the wiper is at P form which path would the current travel, how to determine it? \$\endgroup\$ – On the way to success May 14 '15 at 15:59
  • \$\begingroup\$ By thinking about it. The path would be through both the bare wire and the 10Ω resistor into the wiper, and then through the 1000Ω of the pot. \$\endgroup\$ – Ignacio Vazquez-Abrams May 14 '15 at 16:01
  • \$\begingroup\$ So why you didn't take the equivalent resistance between 1000 ohms and that 10 ohms resistor which is parallel with 1000 ohms when wiper is at P? \$\endgroup\$ – On the way to success May 14 '15 at 16:04

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