[Manager123 (OP)]

Im really confused with this question, newbielink:https://www.dropbox.com/sh/v6ydqbfrg20whtb/ZWR-r9ZOSH?lst#f:q17.JPG [nonactive]

the way i did it was like this  newbielink:http://www.s-cool.co.uk/a-level/assets/learn_its/alevel/physics/Resistance/internal-resistance-emf-and-potential-difference/Finding%20the%20internal%20resistance.gif [nonactive]

However the voltmeter is over the battery, so does this mean that its the opposite and a positive gradient

[evan_au]

The answer just gives you one quadrant to graph the results, so it presumes that the voltmeter V and current meter A are connected to give positive readings.

The graph you give looks right:

• When there is zero current, the voltage measured is ε Volts
  
• When the variable resistor=0, the voltage will be zero, and the current will be at a maximum = ε/r Amps.
  
• The equation of the line is V=ε-rI
  
• But the gradient is "-r", not "r", giving a positive resistance

As a "sanity check", this looks right because, with realistic passive components:

• Resistors are ≥ 0 Ohms
  
• The battery output power is finite:
  
  • If you put too much load on it, the power output (VxA) drops to zero because V=0
    
  • If you don't put any load on it, the power output (VxA) is zero because I=0
    
  • There is some maximum output power in the middle, where the variable resistor is the same as r
• The idea of having a circuit where the slope of the line is positive means that as you increase the load, the output voltage also increases
  
  • So if you reduced the load to zero, the battery output power would be infinite!
    
  • This is quite unlike ordinary batteries!
    

PS: This assumes "ideal" measuring instruments: A Voltmeter with infinite impedance, and an Ammeter with zero impedance.

[syhprum]

Ohms law is of course a poor representation of how things behave in the real world if Manager123 measured the ratio of current to voltage in his lamps he would find that it varies by a factor of ten to one depending upon how much current is flowing.