1. Relationship between V & I
If the temperature is kept constant, we can study the relationship between V & I.
We use the following circuit to study this relationship:
Relationship I, V & R
By changing the number of cells or by using a rheostat, the potential difference across the resistor will change & the current in the resistor changes accordingly. A V
Take the ammeter readings for different voltmeter readings and then draw a graph of V vs I for the resistor.

2. Relationship between V & I
A graph of V vs I can now be drawn for these sets of readings.
0,610
4,6
0,467
3,5
0,307
2,3
0,160
1,2
I in amperes
V in volts
From this graph we see that the gradient or slope is constant and V ∝I and the gradient gives us the resistance of the resistor 5 3 1 V V
V I I
Gradient = = R
,1 0, ,5 =
7,5 Ω I

3. Ohm’s Law
Ohm's law
Since V ∝I at constant temperature, we can see that the resistance is thus staying constant.
From this we can state Ohm’s Law:
The current in a metallic conductor is directly proportional to the potential difference across its ends, provided the temperature remains constant.
The unit of resistance is the V.m-1 also called the ohm (Ω).
A conductor has a resistance of 1Ω if the current in it is 1A when the potential difference across the ends is 1V.
Ohm's law
Ohm's law Click here

4. Equations for finding I
The following equations may be used to find the current in a circuit:
I =
Vemf
Rtot
I =
V resistor
Rresistor
R = V/I
Be careful not to ‘mix & match’ these variables

5. Special concepts about circuits
Resistors in series:
Current same at all points
V for whole circuit = sum of V across each resistor
Vtot = V1 + V2 + V3
Same V across identical resistors
Unequal resistors split Vtot unequally – with higher resistance having the higher V.
Circuit Construction Kit (DC Only) - Electricity, Circuits, Current - PhET

6. Special concepts about circuits
Resistors in parallel:
V across each is the same
I = i1 + i2 + i3
Identical resistors carry same current
Unequal resistors carry unequal currents with the smaller the smaller resistor carrying larger current
Combinations of resistors Click here
Now try as many electrical circuit problems as you can find.
i1 =
I x R r
Current in parallel branch

7. Temperature & resistance
The resistance of a resistor is determined by: R =
V I
The resistance of a conductor usually remains constant – unless it becomes hot – when its resistance increases.
However, at very low temperatures – certain substances become ‘superconductors’ – where they have virtually no resistance at all.
Temperature affecting resistance

8. Temperature & resistance: Ohmic & non-Ohmic conductors
An Ohmic conductor is one that obeys Ohm’s law i.e. when the V is changed across the conductor, so the I through the conductor changes proportionally – provided the temperature remains constant.
A non-Ohmic conductor does not obey Ohm’s law. Its resistance increases as the temperature of the resistance changes.
Filament – non-Ohmic conductor
Resistor – Ohmic conductor

9. Graphs for Ohmic & non-Ohmic conductors
Resistance and temperature
Ohmic and non-ohmic conductors