Electricity

Electrical Current (definition, units)

• The rate of flow of charge.

• Measured in ampères(A)

• Normally a flow of electrons in metals or a flow of ions in electrolytes

Electrical Current (equation with t in it)

I = ΔQ/Δt = charge transfered (coloumbs) / time (seconds)

Charge of an electron

-1.6×10^-19 Coulombs (=-e)

Elementry charge

1.6×10¹⁹ C

Kirchhoff’s 1^st law

At any point in an electrical circuit, the sum of currents into that point is equal to the sum of currents out of that point (electrical charge is conserved)

Conventional current

The ‘flow of positive charge’ - it is in the opposite direction to the movement of the electrons in the circuit.

Mean drift velocity

The average velocity of the charge carriers due to the applied electric field. It has to be an average because they’re often moving randomly in all directions.

Equation for drift velocity

I = Anev

Current = Cross-sectional area × number density × elementry charge × mean drift velocity

Number density

Number of charge carriers per metre³

Potential difference

The energy per unit charge transferred from electrical energy to other forms (heat, light, etc.)

Volt

• 1 V is the p.d. across a component when 1 J of energy is transferred per 1 C passing through the component

• The energy transferred per unit charge.

• Unit of p.d. and e.m.f

Electromotive force (e.m.f)

The energy per unit charge transferred from chemical energy (or other forms like light, heat, movement etc.) to electrical energy

Kirchhoff’s 2^nd law

In a closed loop of an electrical circuit, the sum of the e.m.f.s is equal the sum of the p.d.s

Equation for total resistance of resistors in series

R_T = R₁ + R₂ + …

Equation for resistors in parallel

1/R_T = 1/R₁ + 1/R₂ + …

Ohm’s law

The potential difference across a conductor is directly proportional to the current in the component as long as its temperaure remains constant

Equations linking resistance and resisivity (symbol & word)

R=ρL/A

Resistance(Ω) = resistivity(Ωm) × length of wire(m) / cross-sectional area(m²)

(open) switch circuit symbol

(closed) switch circuit symbol

Cell circuit symbol

Battery circuit symbol

Diode circuit symbol

Resistor circuit symbol

Variable resistor circuit symbol

Lamp circuit symbol

Fuse circuit symbol

Voltmetre circuit symbol

Ammetre circuit symbol

Thermistor circuit symbol

Light dependant resistor (LDR) circuit symbol

Light emitting diode (LED) circuit symbol

Capacitor circuit symbol

IV characteristics of resistors

• P.d. is directly proportional to the current through it (V∝I).

  • Ohmic conductor

  • The resistance is constant.

• The resistor behaves in the same way regardless of the polarity.

IV characteristics of filament lamps

• P.d. is not directly proportional to the current through it.

  • non-ohmic component

  • the resistance is not constant.

• Behaves in the same way regardless of the polarity.

• Resistance of the filament lamp increases as the p.d. across it increases

IV characteristics of diodes

• P.d. is not directly proportional to the current through it.

  • non-Ohmic component

  • the resistance is not constant.

• The ____ behaviour depends on the polarity.

• Below the threshold p.d. the resistance is very high - infinite for practical purposes (e.g. at A)

• At the threshold p.d. (at B) the resistance gradually starts to drop.

• Above the threshold p.d. the resistance drops rapidly (e.g. at C) and the ____ has very little resistance.

IV characteristics of thermistors

• P.d. not directly proportional to current. As such:

  • it is a non-ohmic component

  • resistance is not constant

• Behaves in the same way regardless of the polarity.

• Resistance of the thermistor decreases as current increases.

  • Temperature increases as current increases.

  • This causes an increase in number density and so a drop in resistance.

  • This can be confirmed by comparing R = V/I at various points on the graph (resistance is NOT 1/gradient)

Potential divider

Electrical circuit that uses resistors to deliver only a proportion of the voltage from a battery to a component in order to produce a specific output

Potential divider equation

V_out = V_in × R₂ / (R₁ + R₂)

Where R₁ + R₂ = R_T

Similaraty and difference between e.m.f. and p.d.

• Both are measured in volts/ defined as energy transferred per unit charge

• Charges are losing energy for ___ and gaining energy for ___

Definition of the kilowatt hour

1 ___ is the energy transferred by a 1kW device in a period of 1 hour

How an electron gun produces a beam of high speed electrons

• Electrons are emitted from the hot wire/filament at the rear of the electron gun through thermionic emission

• There is a large p.d. between the filament and an anode.

• Electrons are accelerated towards the anode.

• They pass through a hole/gap in the anode.

Equation relating work done on charged particles and their gain in kinetic energy

eV = ½mv²

work done on electron = gain in KE

Internal resistance

The resistance of a source of e.m.f (e.g. a cell) due to its construction, which causes a loss in energy/voltage when the charge passes through the source

Lost volts

The potential difference across the internal resistor of a source of e.m.f

Finding Internal resistance practical (with circuit and equations)

Diagram:

• Circuit shown above

Method:

• Set up the circuit as above.

• Record the voltage across and current through the variable resistor in a table

• Vary the resistance (by adjusting the variable resistor) and record the voltage across and current through the variable resistor each time.

• Make sure to record at least 5 pairs of voltage and current readings across a decent range.

Analysis:

• Plot a graph of V against I from the recorded values, drawing a line of best fit that extends all the way back to the y-axis to find the y-intercept. Then calculate the gradient of the line of best fit

• Using Kirchhoff’s 2^nd law, ε = IR + Ir. V = IR, so ε = V + Ir. Rearranging this gives V = -rI + ε

• As such the gradient of our line of best fit = -r (so r = -1 × gradient), and the y-intercept = ε.

Safety:

• Be careful handling the battery as it can be hot from the current

• Do not set the variable resistor too close to zero resistance as this will cause the current to be larger. Too large of a current can cause the battery to overheat which could burn you or even start a fire

Design a circuit for a light meter to monitor changes in light intensity. The meter reading must rise when the light intensity increases. The incident light may cause the resistance of the LDR to vary between 1500 Ω and 250 Ω.

• You can use either a 1500Ω or a 750Ω fixed resistor

• You can use either a ammeter or a voltmeter

Draw a suitable circuit and explain why the reading on the meter increases with increasing light intensity and which of the two fixed resistors gives the largest scale change on the meter for the change in light intensity.

Circuit:

• As shown in image if using voltmeter, otherwise ammeter should be in series

Action of circuit:

• When light intensity increases resistance of LDR falls

• So p.d. across resistor increases (or current in circuit increases) so the meter reading increases

Meter and sensitivity:

• Need the largest change in voltage or current for a given

  change in light intensity

• Choose resistor of 750Ω to give the largest change on the

  meter

Electronvolt

• Energy transferred to or from an electron when it passes through a potential difference of 1 volt

• 1 eV is equivalent to 1.60 × 10-19J