Chp 10: Electrical circuits

Physics Year 1 OCR A Level

Kirchhoff's First Law

the sum of currents into a junction equals the sum of currents out of a junction

Kirchhoff's Second Law

In any circuit, the sum of the electromotive forces is equal to the sum of pds around a closed loop

What law of conservation is used for KL1?

Law of conservation of energy, which is applied to electric circuits, so law of conservation of charge

sum of emf \=

sum of pds around a closed loop

Current in series circuit

Is the same everywhere

Voltage in series circuit

split according to components resistance

Voltage in a parallel circuit

voltage is the same across each closed loop

in a parallel circuit the sum of the voltages in each closed circuit loop is equal to

the total emf of the power supply

If the emfs are connected in opposite ways to each other...

you subtract them

Parallel circuits: the greater the resistance of the branch

the lower the current that goes into it, because V\=IR and V stays constant for the branches

If there are several components in a loop, the sum of the pds across these components is equal to

the emf supplied by the battery

Equation for resistors in series

R\=R1 + R2 + R3

Explain the equation for resistors in series

• According to KL2 V=V1+V2

• so IR= IR1 + IR2

• I is a constant according to KL1 so R=R1+R2

Equation for resistors in parallel

1/R \= 1/R1 + 1/R2

Four key equations

Q\=It, E\=VQ (E\=VIt or W\=VIt), P\=VI, V\=IR

terminal pd

pd measured at the terminals

What is the difference between the emf and the terminal pd called?

lost volts

electromotive force\=

terminal pd + lost volts, I(R+ r)

define internal resistance

The resistance of a source of emf due to its construction, which causes a loss in energy/voltage as the charge passes through the source

lost volts \=

I x r, r\=internal resistance

Connecting cells in series...

increases emf but also increases internal resistance

Connecting cells in parallel..

produce same emf as just one cell but provides greater current due to the reduced internal resistance

What does a battery of negligible internal resistance mean?

emf\=terminal pd

Describe an experiment to determine internal resistance

• connect an ammeter and variable resistor/potentiometer and switch in series and a voltmeter in parallel around the variable resistor

• with switch open, record the reading V on the voltmeter

• set variable resistor to max value, close switch and record V and I

• make sure to open the switch between readings to avoid running the battery down/heating the circuit

• vary the resistance of the variable resistor for 8 readings and take an average for each resistance

• Plot V= -rI + E (V against I)

• the negative gradient is the internal resistance

Why is there a cell and a resistor labelled r in a circuit?

The resistor isn't really there, it represents cell's internal resistance

Why do car batteries and many rechargeable batteries have small internal resistances?

allows them to be recharged using higher currents without overheating or wasting a lot of energy

Why do high voltage power supplies in classrooms have a very high internal resistance?

prevents power supply from delivering a fatal electric current

emf

energy transferred by the power supply per unit charge

What is the relationship between work done, emf and charge?

W\=eQ

Potential dividers

circuits that produce an output voltage as a fraction of its input voltage

Purposes of potential dividers

Split PD of power source between 2 or more components

Potentiometer symbol

box with arrow pointing to it

When using a potential divider, how to calculate what reading will show on a voltmeter? (potential divider equation)

look at what resistor the voltmeter is over, R1 and other resistor will be R2
- V out \= R1/R1+R2 x V in

Loading a potential divider

connecting a component in parallel to the resistor that has a voltmeter over it in a potential divider circuit

How to produce a varying V out in a potential divider?

replace fixed resistor with a variable resistor

What is a potentiometer?

a variable resistor with 3 terminals and a sliding contact

If I have a potentiometer and I slide the dial towards the left side, what happens to the output voltage on the left?

increases because resistance decreases

State 4 advantages of using a potentiometer over a potential divider

can be made very compact, uses fewer components, can be easily turned into a rotary dial, allows full range of output potential difference from 0v to V in

Describe a graph of V against I that describes how the terminal pd of a supply changes with the amount of current drawn

y intercept \= emf supplied
negative gradient, not very steep, linear relationship, as voltage decreases, current decreases

How will VI graph change if you double emf and have the same internal resistance?

double y-intercept, same gradient: changes y intercept in same way

How will VI graph change if you have the same emf and have half the internal resistance?

same intercept, half the gradient: changes the gradient in the same way

What does a circuit with a potential divider that can be used as a temperature sensor so that output voltage increases with increasing temperature look like?

Thermistor in circuit, but since temp and resistance are inversely proportional, put voltmeter over the other resistor

When you draw a circuit that includes internal resistance, denoted r, how should you draw it?

Draw resistor next to battery with little r above it and draw a dotted box around battery and resistor to show they are the same thing