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: A 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. V Take the ammeter readings for different voltmeter readings and then draw a graph of V vs I for the resistor. Relationship I, V & R 1

Relationship between V & I 0,6104,6 0,4673,5 0,3072,3 0,1601,2 I in amperes V in volts A graph of V vs I can now be drawn for these sets of readings. V I 0 0,1 0,3 0,5 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 R= VIVI Gradient V I = =7,5 Ω 2

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 lawOhm's law Click here Ohm's law 3

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

Special concepts about circuits Resistors in series: Current same at all points V for whole circuit = sum of V across each resistor V tot = V 1 + V 2 + V 3 Same V across identical resistors Unequal resistors split V tot unequally – with higher resistance having the higher V. Circuit Construction Kit (DC Only) - Electricity, Circuits, Current - PhET 5

Special concepts about circuits Resistors in parallel: V across each is the same I = i 1 + i 2 + i 3 Identical resistors carry same current Unequal resistors carry unequal currents with the smaller the smaller resistor carrying larger current i 1 = I x R r Now try as many electrical circuit problems as you can find. Current in parallel branch Combinations of resistorsCombinations of resistors Click here 6

Temperature & resistance The resistance of a resistor is determined by: R = VIVI 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 7

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. Resistor – Ohmic conductor Filament – non- Ohmic conductor 8

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