A fixed resistor A filament lamp An LED Sketch an I/V graph for: Now underneath think about what a R/V graph would look like for:

Resistivity 21/08/2018 LO: Investigate how resistance varies with length and cross-sectional area Define resistivity and practice using the formula

Resistance or Resistivity? In previous lessons we have said that resistance is the obstruction offered to the flow of current (ratio of potential difference across component, to the current through component.) Resistivity is the obstruction offered to the flow of current per unit area of the conductor. Resistance is the property of the object (e.g. copper wire), whereas resistivity is the property of the substance (e.g. copper).

Resistance or Resistivity? So for example take two objects A and B made of copper. Both are of a different size. The resistance (total obstruction to flow) of A & B will be different. But the resistivity (obstruction per unit volume) will be the same.

Resistance or Resistivity? The resistance of a material is proportional to its length, i.e. the longer it is the higher R; R ∝ L The resistance of a material is inversely proportional to its cross sectional area, i.e. the thicker the wire the lower R. R ∝ L/A

Proportionalities R ∝ L/A To turn this proportionality into an equation we need to add a constant of proportionality (k). E.g. the time a car is driven for is proportional to the distance it will travel. The constant of proportionality is the speed it is travelling. The amount of money I earn is proportional to the time I work. The constant of proportionality is the hourly wage.

Proportionalities R = ρL / A To turn this proportionality into an equation we need to add a constant of proportionality (k). R = ρL / A

Can you re-arrange to find ρ? Resistivity R = ρL / A Where; R = Resistance (Ω) ρ = Resistivity (Ω m) L = Length (m) A = Cross-sectional area (m2) Can you re-arrange to find ρ?

Resistivity The resistivity of a material and the conductivity of a material are inversely linked. Good conductors have a low resistivity, while poor conductors (insulators) have resistivities that can be 20 orders of magnitude larger. A low resistivity indicates a material that readily allows the movement of electric charge.

Using a Micrometer Object Thickness / mm 1 2 3 Avg. 10p coin Hair

Experiment: Finding the resistivity of constantan wire Experiment: Finding the resistivity of constantan wire. Method: Connect one of the wires to a 1.5V battery. Measure current at varying lengths (l) of wire and calculate resistance (R) for each. Results: Plot a graph of resistance (y-axis) against length (x-axis). Conclude: How does resistance vary with length (l)? Use a proportional sign. What feature of the graph provides the resistivity?

Gentleman Value for ρ Placing Ed 5.89x10-7 Doddy 5.64x10-7 Timmy! 5.28x10-7 3rd Place Nick 5.63x10-7 Tom 5.47X10-7 Ruari 6.14x10-6 Clayton 5.27x10-7 2nd Place Adrian 5.67X10-7 Dan Jake 4.38x10-7 Munvi 6.90x10-7 Ollie 5.06 x 10-7 1st Place! Femi 6.92x10-7 Joe 5.64X10-7 Hugh 5.43X10-7

Results Length / m V/V I/A R/Ω Diameter of wire = Radius of wire = x 10-3m A = m2 Length / m V/V I/A R/Ω 0.200 0.300

Calculating Resistivity Resistance (Ω) Main sources of error? Length (m)

Calculating Resistivity Assumptions Constant temperature Constant cross-sectional area Plot should indicate a linear relationship. Where the gradient is equal to resistivity / cross sectional area. Therefore resistivity = gradient X A Resistance (Ω) Length (m)

Calculating Resistivity What do the different colours represent? Resistance (Ω) Length (m)

Calculating Resistivity If ρ = gradient X A Then the larger the cross-sectional area the flatter the gradient as two numbers must multiply to make the same value for resistivity. Resistivity does not change with cross sectional area because it is independent of the size / volume. It is a property of the material not the object! Resistance (Ω) Length (m)

2.85Ω E.g. Coppers resistivity is 1.68x10-8Ωm at 20oC. What is the resistance of a sample of copper that is 3.00m long and has a diameter of 0.15mm? 2.85Ω

Values for Resistivity If the value for resistivity in a conductor such as constantan is in the order of 5 x 10-8 Ω m then how many metres of the material would be needed to achieve 1 ohm of resistance (where the diameter is 0.5mm) Why would the answer to number 1 not be suitable for constructing a 10kΩ resistor? How could the current material be made more suitable? What material might be more suitable alternative?

Values for Resistivity

Practice makes perfect! Resistivity Worksheet Finished? Questions Pg 103

How does the resistivity of conductors vary with temperature? Why? Prediction: How does the resistivity of conductors vary with temperature? Why?

Resistivity and temperature Explain why resistivity is proportional to the temperature of the conductor. Key words to include; Turbulent Conduction electrons Ions Temperature Collision

Resistivity A low resistivity indicates a material that readily allows the movement of electric charge. Under high temperatures the collisions between electrons and ions in the conductor makes the ions move rapidly. The rapid movements of the turbulent ions then creates further resistance for the conduction electrons moving through the wire.

Negative temperature coefficient (NTC) thermistor Draw a circuit to investigate its current/voltage characteristics. Investigation: Using a voltmeter and an ammeter investigate how resistance and therefore resistivity varies with temperature for an NTC thermistor. Dimensions of NTC Thermistor Chip: 0.25mm depth, 0.25mm width, 3mm length.

Conclusions: The resistance (and hence resistivity) of an NTC thermistor _________ as temperature ________. NTC thermistors are made mostly of________. The physical change in temperature permits more... All semiconductors behave in this way when temperature is increased.

What does each line represent and why? Temperature / 0C Resistivity / m

Metal – more ion vibration (when hotter) impedes electrons Insulator – thermal energy releases more charge carriers Semiconductor – more ion vibration outweighed by more free charge carriers Temperature / 0C Resistivity / m insulator semiconductor metal

Practice makes perfect! Review Resistivity Worksheet – Try a few again and see if you can improve. ASK SOMEONE to help! Questions Pg 103 in OCR books. You may fine P140 – 142 in AS/A2 Physics helps consolidate the knowledge. Finished? Try Q’s on 144 of AS/A2 Physics.

LDR – Light dependent resistor Experimental Write-up: Circuit diagram to show how you investigated the current/voltage characteristic for a LDR. Complete experiment varying light intensity (think about how to do this quantitatively). There are a lot of random errors so repeats are needed! Tabulate V and I to find R. Calculation of A for photosensitive chip using info on board. Calculate resistivity for each value. Graph light intensity (or similar) against resistivity. Conclude using key words; temperature, light, ion, vibration, electron, charge carrier, liberated. Sources of error identified and discussed Thickness of cadmium sulphide track = 0.41mm Length of cadmium sulphide track = 13.4mm

Value for light intensity follows the inverse square law. Intensity: 1 / distance2

Conclusions: The resistance (and hence resistivity) of an LDR _________ as light intensity _________. The resistance (and hence resistivity) of an NTC thermistor _________ as temperature ________. NTC thermistors are made mostly of________. In both cases the physical change (temp or light) allows more... All semiconductors behave in this way when temperature is increased.

Practice makes perfect! Review / Complete question sheet on Components. Try your hand at Thermistor question sheet. Answer the Q’s on the Thermistor / LDR section in text book (page X). Make a hat that says “I’m jolly clever” and parade around the class.