Resistance

1.5.1 Voltage
Voltage is de ned as the energy change per unit charge between two points in the circuit, with the formula:

Please note that this is not in the formula booklet.
1.5.2 Ohm’s Law and Resistance
Ohm’s Law states that the current owing through a metal at constant temperature is directly proportional to the p.d. across it. Since we know that resistance is caused by the collisions between free electrons and ions, we nd a constant drift velocity and we can de ne resistance as the ratio of voltage across divided by current through a component, with the formula:

1.5.3 Power
Power is de ned as the rate at which energy is transferred, used, or transformed, with the formulae:
Power = Current×Voltage
P = IV
(W) = (A)(V)

1.5.4 Resistivity
Resistivity is de ned as the resistance of a material per metre3 from one end to the other, with the formula:

1.5.5 Finding Resistivity Experimentally
Resistivity can be found experimentally by using an ammeter, voltmeter, and a ruler or caliper, simply use the voltmeter and ammeter to nd the current and voltage across the block of material which is connected to a circuit, and we can nd that the resistance from V = IR and then use the ruler/caliper to nd the length and area of the component, allowing you to nd the L and A from R = ρL A , so along with the R you can nd the resistivity (ρ).

1.5.6 Finding out the E ect of Temperature on Resistance of a Metal Wire
1. Apparatus and Materials required: (a) Power supply, DC – ≈12V and at least 4A (b) Rheostat – 10-20 Ohms, rated at 5A at least (c) Aluminium container (e.g. disposable food container) (d) Ammeter – 0-5A DC (e) Voltmeter – 0-10V DC (f) Leads – 6 × 4mm (g) Crocodile clips – 2 (h) Coil of copper wire (the wire may release hazardous fumes, only perform in a well ventilated laboratory)
2. Method:
(a) Connect up a simply circuit that looks like this:

(b) (c) Adjust the power supply until about 4-5A and then switch of the circuit as soon as possible. (d) Once the circuit has cooled down again (which should take around a minute), switch the circuit on again. During the next half-minute or so, take several ammeter and voltmeter readings, the current will change quickly as the coil heats up. (e) Repeat the experiment with the coil of wire suspended in water in the container and the water should be kept well stirred (with an insulting stirrer to prevent you from short-circuiting the device).
3. Record a graph of the two sets of readings for current and voltage, the graph of the one suspended in water should be exhibit Ohm’s Law with a straight line correlation showing that resistance is proportional to p.d. and the other should graph to a curved line which is increasing in gradient, which shows that the resistance increases with temperature.
4. This experiment can be extended/improved by using a water bath to test temperatures between 0◦C and 100◦C

1.5.7 Superconductivity and Superconducting Transition Temperature
Superconductivity is where a material does not exhibit any resistance to the ow of electricity. Not all materials exhibit superconductivity, but in those that do, the superconducting transition temperature is the temperature below which a material will conduct without resistance. Most materials that are super-conductive have extremely low transition temperatures, usually a few degrees above absolute zero (−273◦C), but some special materials, known as high temperature superconductors, have transition temperatures above the boiling point of nitrogen (−196◦C) and can therefore be kept cool with liquid nitrogen which massively reduces the cost of keeping these materials below the transition temperature and as a result, superconducting. Superconductors are used in particle accelerators, tokamaks and magnetic resonance imaging machines and are expected to soon be used in some large motors and generators