topic 4: electrical currents

filament lamp I-V graph

semiconductor diode I-V graph

ntc thermistor I-V graph

determining conductivity + explanation

insulator: conduction band empty ; valence band full ⇒ large band gap

semiconductor: conduction band < valence band ⇒ small band gap

• an electron leaving the valence band leaves a positive hole, which appears to move the opposite way

• heating a semiconductor promotes many more electrons across the gap, so band gap decreases and its resistance falls

• an LDR uses light and an NTC thermistor uses heat to boost the number of conduction electrons

conductor: conduction band = valence band ⇒ no band gap

emf (of cell) definition

energy transferred (from chemical energy to electrical energy) per unit charge passing through the cell

reason for open and closing switch

opening switch between readings prevents the cell from heating up due to prolonged current flow, ensuring its internal resistance r remains constant

emf vs pd

emf: energy is transferred to electrical energy put into the circuit

pd: energy is transferred from electrical energy taken out of the circuit

ohm’s law

the current through a component is directly proportional to the pd across it, provided the temperature stays constant

investigating resistivity

METHOD

1. Measure diameter at 5-10 points; take the mean

2. Clamp the wire's left end at the ruler's zero

3. Attach the flying lead at 0.25 m; set 6.0 V

4. Record I, then switch off at once

5. Repeat in 0.25 m steps to the full length

REDUCING UNCERTAINTY

• Average 5-10 diameters in right-angled pairs

• Use small currents as resistivity depends on temperature

• Switch off between readings

• Use the longest wire practical

resistance without emf

1. Metals have a regular lattice of positive ions with free (delocalised) electrons that can move through the whole structure

2. Without an emf the electrons move randomly, so the average position of all the charge is stationary and there is no current

3. An emf sets up an electric field that pushes electrons towards the positive end. Their slow overall movement is the drift velocity

4. The transport equation I = nAve links current to the carrier density, the area, the drift velocity and the charge

5. Resistance is caused by collisions between the drifting electrons and the vibrating lattice ions, which slows the electrons down

6. Higher temperature means more vigorous lattice vibrations, more collisions, a lower drift velocity and therefore greater resistance

effect of temperature on carrier density

METAL

• high carrier density

• when heated: carrier density falls very slightly from thermal expansion ⇒ more lattice collisions ⇒ resistance rises

SEMICONDUCTOR

• small carrier density

• when heated (light for LDR): carrier density rises enormously as electrons gain enough energy ⇒ more electrons to conduction band ⇒ band gap decreases ⇒ extra carriers outweigh collisions ⇒ resistance falls

superconductivity

Below a critical temperature some materials show superconductivity: zero resistivity and no energy dissipated as heat

Explanation:

• temperature of the material decreases the thermal energy decreases lattice ions vibrate with smaller amplitudes

• when the material is cooled below its critical temperature, the lattice vibrations become so small that electrons can pass through the lattice without colliding with any ions

• because there are no collisions between the conduction electrons and the lattice ions, there is no opposition to the flow of charge

• Therefore, the electrical resistance drops abruptly to zero

$V_{out}$ equation

V_{out}=V_{\imaginaryI n}\times\frac{R_2}{R_1+R_2}

$$\frac{V_1}{V_2}=\frac{R_1}{R_2}$$

internal resistance equations

$$\char"0190 =I\left(R+r\right)$$

$$V=\char"0190 -Ir$$

$$\char"0190 =V+Ir$$