3- Electric Circuits

Potential Divider

A circuit with a voltage source and a couple of resistors in series

What does a potential divider do

Split the potential difference in the ratio of the resistances

Why are potential dividers used

If you need a potential difference lower than the voltage source

Potential Divider equation

V_out = (R₂/R₁+R₂) x V_s

What are potential dividers mainly used for

Calibrating voltmeters

How can the output voltage of a potential divider be varied

Using a variable resistor

How does increasing the resistance of R₁ affect the output voltage of a potential divider

It will decrease

Why are voltmeters calibrated using potential dividers

You can vary the output voltage using a variable resistor and measure if the value on the voltmeter is correct

Explain why voltmeters are mainly used for potential dividers and not other devices

When attached to the resistor, the device will behave like a resistor in parallel, where the total resistance will always be less than R₂ so the output voltage is slightly less. Voltmeters have a high resistance, making the decrease in total resistance negligible

Explain how a light sensor works

The circuit is a potential divider using an LDR. At higher light levels, the resistance will be lower, giving a higher output voltage

Explain how a temperature sensor works

The circuit is a potential divider using an NTC thermistor. As temperature increases, resistance decreases, giving a higher output voltage

Uniform wire

The same cross-sectional area and material throughout

Flying lead

Wire that curves

Explain how the length of a wire affects potential difference across the length

The resistance of a uniform wire is proportional to its length. This means that the potential difference of a wire is proportional to its length

How does increasing the length of a wire affect the potential difference across that wire

Increases

How does a potentiometer work

One variable resistor is used instead of 2 resistors, but a slider acts to separate it into 2. The slider changes the length of the resistor, which changes the output voltage

Potentiometer

Gives a variable voltage

Is charge in a circuit used up

No

Kirchhoff’s First Law

The total current entering a junction = the total current leaving it

Explain Kirchhoff’s First Law

Current is the rate of flow of charge and as charge in a circuit isn’t used up or lost, the same charge will flow out of a junction that went in

What may Kirchhoff’s Laws be called instead

Conservation laws

Kirchhoff’s Second Law

The total e.m.f around a series circuit = the sum of the p.d.s across each component

Kirchhoff’s Second Law equation

ε = ΣIR

Explain Kirchhoff’s Second Law

Energy transferred to a unit charge is e.m.f and energy transferred from a unit charge is potential difference, so these must be equal in a closed loop

Current in a series circuit

The same at all points

Electromotive force in a series circuit

Split between components

Resistance in a series circuit

Total resistance shared between all components

Current in a parallel circuit

Split at a junction

Potential difference in a parallel circuit

Equal for each loop in parallel

Resistance in a parallel circuit

1/R_total = 1/R₁ + 1/R₂ + 1/R₃…

Explain the resistance in a series circuit

e.m.f is split across components by Kirchhoff’s 2nd Law so ε = V₁ + V₂ + V₃. V = IR, so IR_total = IR₁ + IR₂ + IR₃. Cancel I for R_total = R₁ + R₂ + R₃

Explain the resistance in a parallel circuit

The current for each resistor is spread between each loop. For each loop it I = V/R so the total current for the loops = V/R_total = V/R₁ + V/R₂ + V/R₃. Cancel out V such that 1/R_total = 1/R₁ + 1/R₂ + 1/R₃

How does resistance in circuits occur

Electrons colliding with atoms and losing energy

Internal resistance

the resistance of a battery

Explain how batteries can have internal resistance

Batteries use chemical energy to make electrons move- these electrons collide with atoms in the battery- losing energy, so causes resistance

Why do batteries warm up after use

Internal resistance

Load resistance

Total resistance of components in the external circuit

Electromotive force

The total work the battery does on each coulomb of charge

What is electromotive force measured in

Volts

What is the symbol for electromotive force

ε

Terminal potential difference

The work done when one coulomb of charge flows through the load resistance

With no internal resistance, how would the relationship between terminal potential difference and electromotive force change

They would be equal

Lost volts

Work done per coulomb of charge overcoming internal resistance

Load resistance symbol

R

Internal resistance symbol

r

Terminal potential difference symbol

V

Lost volts symbol

v

Electromotive force equation 1

ε = V + v

Electromotive force equation 2

ε = I(R + r)

Electromotive force equation 3

ε = V + Ir

Experiment to investigate electromotive force and internal resistance

1- Vary the current using a variable resistor

2-Measure the potential difference across the cell for different values of current

3- Plot a graph of potential difference against current

4- The gradient is -r and the y-intercept is ε

Explain an easier way to measure ε of a power source

Connect a voltmeter across a power source. They have a high resistance, so only a small current will flow through them, meaning the value of ε will only be slightly smaller than the true value

Power in circuits equation 1

P = VI

Power in circuits equation 2

P = I²R

Power in circuits equation 3

P = V²/R

Work done in a circuit equation

= VIt

Experiment to investigate the power output of a motor

1- Attach a mass to a motor and connect the motor to a circuit. Close the switch so the motor will turn on, winding the string around the axle and raising the mass

2- Record the time taken for the motor to raise the mass a set distance using a stopwatch and metre ruler

3- Calculate work done against gravity with ΔE_grav= mgΔh, then find power with P = W/t

How to find the efficiency of a motor with a known power

Measure the potential difference across the motor and the current through it to find the input power with P=IV, then find efficiency with useful power output/total power input

I-V characteristic

A graph which shows how the current flowing through a component changes as the potential difference across it is increased

How to change the potential difference and current to investigate the I-V characteristics

Variable resistor

I-V characteristic for a metallic conductor

Directly proportional

How to find resistance from an I-V graph

1/gradient

Are metallic conductors ohmic

Yes

What must be kept constant when investigating I-V characteristics

Temperature

Filament in a lamp

Coiled up length of copper wire

Explain the I-V characteristic of a filament lamp

The current flowing through increases its temperature, increasing resistance

How is charge carried through metals

By free electrons in a lattice of positive ions

Explain how increasing temperature affects resistivity

The lattice of positive ions vibrate more, so electrons collide with them more often and transfer away their kinetic energy. This decreases the speed of electrons, decreasing the mean drift velocity, which is directly proportional to current so decreases current, increasing resistivity.

Resistivity of semi-conductors compared to normal metals

Higher

Explain the resistivity of semi-conductors

Higher as there are fewer charge carriers available

Explain how increasing temperature affects the resistivity of semi-conductors

The increase in temperature provides energy to release more charge carriers, increasing current, decreasing resistivity

How does increasing the temperature of a semi-conductor affect its resistivity

Decreases

How does increasing the temperature of a metal affect its resistivity

Increases

What are semi-conductors used for

Sensors for change in their environment

Semi-conductor examples

-Thermistor

-LDR

-Diode

How does increasing temperature affect the resistance of an NTC thermistor

Decreases

Main type of thermistor

NTC thermistor

NTC thermistor

Negative temperature coefficient thermistor

Draw an I-V graph for a metallic conductor

Draw a I-V graph for a filament lamp

Draw an I-V graph for an NTC thermistor

Explain the I-V characteristic of a thermistor

As voltage increases, current increases, increasing temperature, decreasing resistance

Explain how heating thermistor works

This gives electrons enough energy to escape from their atoms, so there are more charge carriers available, increasing current, decreasing resistance

Why aren’t semiconductors’ resistance increased due to the vibrations of ions

The effect of the vibration of ions is much less than the release of more charge carriers

How does a greater light intensity affect an LDR’s resistance

Decreases

Explain how an increase in light intensity affects an LDR’s resistance

The light provides energy to electrons to escape out of their atoms, meaning more charge carriers, so a higher current can flow, decreasing resistance

Filament lamp circuit symbol

Variable resistor circuit symbol

Thermistor circuit symbol

LDR circuit symbol

Diode circuit symbol

LED circuit symbol

Forward bias

The direction which the current in the diode can flow

Threshold voltage

The voltage most diodes require in the forward direction before they will conduct

Normal threshold voltage for a diode

0.6

Explain why current doesn’t flow in reverse bias

the resistance is very high, so the current is tiny

Draw an I-V graph for a diode

Draw an I-V graph for an LDR

Current equation

I = ΔQ/Δt

Current

The rate of flow of charge