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Resistance & Resistors (DP IB Physics: SL)

Revision Note

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Resistance

  • As electrons move through the metal wire of a circuit (or any other component), they transfer some of their electrical potential energy to the positive ions of the metal

Electrons and resistance, downloadable AS & A Level Physics revision notes

Free electrons collide with metal ions which resist their flow

  • This energy results in an increase in the kinetic energy of the lattice
  • Which means a higher internal energy of the metal
  • The macroscopic result of this transfer is the heating up of the wire
  • Some metals heat up more than others
    • The higher the heating, the higher the resistance
    • Wires are often made from copper because copper has a low electrical resistance

  • The resistance R of a component is defined as:

The ratio of the potential difference across the component to the current flowing through it 

  • It is calculated as follows:

  • Where:
    • V = potential difference in volts (V)
    • I = electric current in amperes (A)
    • R = resistance in ohms (Ω)

  • This means that the higher the resistance of a component, the lower the current flowing through it and vice versa
  • In terms of SI base units: 1 Ω = 1 kg m2 s–3 A–2

Worked example

A charge of 5.0 C passes through a resistor at a constant rate in 30 s. The potential difference across the resistor is 2.0 V.

Calculate the resistance R of the resistor.

Step 1: Write down the known quantities 

    • Charge, Δq = 5.0 C
    • Time, Δt = 30 s
    • Potential difference, V = 2.0 V

Step 2: Write down the equation for the resistance R 

Step 3: Calculate the current I from the charge and time 

Step 4: Substitute the numbers into the above equation 

I = 0.17 A

Step 5: Substitute this value of the current into the equation for the resistance given in Step 2

R = 12 Ω

Resistors in Series & Parallel

Resistors in Series

  • When two or more components are connected in series:

Resistors in series diagram, downloadable AS & A Level Physics revision notes

The combined resistance of the components is equal to the sum of individual resistances

Resistors in series equation, downloadable AS & A Level Physics revision notes

  • This means as more resistors are added, their combined resistance increases and is, therefore, more than the resistance of the individual components

  5-2-2-resistors-in-series_sl-physics-rn

Connecting more resistors in series increases the overall resistance

Worked example

The combined resistance R in the following series circuit is 60 Ω. What is the resistance value of R2?

A.     100 Ω               B.     30 Ω               C.     20 Ω               D.     40 Ω

Step 1: Write down the known quantities

    • Total resistance, R = 60 Ω
    • Resistance of first resistor, R1 = 30 Ω
    • Resistance of third resistor, R3 = 10 Ω

Step 2: Write down the equation for the combined resistance of resistors in series 

R = R1 + R2 + R3

Step 3: Rearrange the above equation to calculate the resistance R2 of the second resistor 

R2 = R – R1 – R3

Step 4: Substitute the numbers into the above equation 

R2 = (60 – 30 – 10) Ω

R2 = 20 Ω

ANSWER: C

Resistors in Parallel

  • When two or more components are connected in parallel:

Resistors in parallel diagram, downloadable AS & A Level Physics revision notes

The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances

Resistors in parallel equation, downloadable AS & A Level Physics revision notes

  • This means as more resistors are added, their combined resistance decreases and is, therefore, less than the resistance of the individual components

  5-2-2-resistors-in-parallel_sl-physics-rn

Connecting more resistors in parallel decreases the overall resistance

Worked example

WE - Resistors in parallel question image, downloadable AS & A Level Physics revision notes

Step 1: Write down the known quantities 

    • Resistance of first resistor, R1 = R
    • Resistance of second resistor, R2 = 2R
    • Resistance of third resistor, R3 = R

Step 2: Write down the equation for the reciprocal of the combined resistance (1/RTOT) of resistors in parallel 

Step 3: Substitute the given quantities into the above equation 

Step 4: Take the reciprocal of the second equation above to get the combined resistance RTOT

ANSWER: D

Examiner Tip

The most common mistake in questions about parallel resistors is to forget to find the reciprocal of RT (i.e. 1/RT) instead of RT. Here is a maths tip to rejig your memory on reciprocals:

  • The reciprocal of a value is 1 / value
  • For example, the reciprocal of a whole number such as 2 equals ½
    • Conversely, the reciprocal of ½ is 2

  • If the number is already a fraction, the numerator and denominator are ‘flipped’ round

Reciprocals, downloadable AS & A Level Physics revision notes

The reciprocal of a number is 1 ÷ number

  • In the case of the resistance R, this becomes 1/R
  • To get the value of R from 1/R, you must calculate 1 ÷ your answer
  • You can also use the reciprocal button on your calculator (labelled either x –1 or 1/x, depending on your calculator)

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Ashika

Author: Ashika

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Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.