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Internal Resistance (CIE AS Physics)

Revision Note

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Internal resistance

  • All power supplies have some resistance between their terminals
    • This is called internal resistance (r)

  • This internal resistance causes the charge circulating to dissipate some energy from the power supply itself
    • This is why the cell becomes warm after a period of time

  • The internal resistance therefore causes a loss of voltage or energy loss in a power supply
  • A cell can be thought of as a source of e.m.f with an internal resistance connected in series. This is shown in the circuit diagram below:

Circuit with e.m.f

Internal resistance circuit, downloadable AS & A Level Physics revision notes

Circuit showing the e.m.f and internal resistance of a power supply

 

  • VR is the terminal potential difference
    • This is the voltage available in the circuit itself
    • Terminal p.d = I × R (Ohm’s law)

  • When a load resistor is connected, current flows through the cell and a potential difference develops across the internal resistance. This voltage is not available to the rest of the circuit so is called the ‘lost volts’
  • Vr is the lost volts
    • This is the voltage lost in the cell due to internal resistance, so, from conservation of energy:
    • Lost volts = e.m.f − terminal p.d
    • Lost volts = I × r (Ohm’s law)

  • The e.m.f is the sum of these potential differences, giving the equation below:

thin space E equals space I R space plus thin space I r space equals space I open parentheses R space plus thin space r close parentheses

  • Where:
    • E = e.m.f (V)
    • I = current (A)
    • R = load resistance (Ω)
    • r = internal resistance (Ω)
  • IR is collectively known as the 'terminal potential difference'
  • Ir is collectively known as the 'lost volts'

Worked example

A battery of e.m.f 7.3 V and internal resistance r of 0.3 Ω is connected in series with a resistor of resistance 9.5 Ω.WE - internal resistance question image, downloadable AS & A Level Physics revision notesDetermine:

a)     The current in the circuit

b)     Lost volts from the battery

Answer:

a)

Step 1: List the known quantities:

  • E.m.f, E = 7.3 V
  • Load resistance, R = 9.5 Ω
  • Internal resistance, r = 0.3 Ω

Step 2: Use the e.m.f equation to determine the current I

E thin space equals space I open parentheses R space plus thin space r close parentheses

I space equals space fraction numerator space E over denominator R thin space plus thin space r end fraction

Step 3: Substitute the values

I space equals space fraction numerator 7.3 space over denominator 9.5 space plus thin space 0.3 end fraction space equals space 0.745 space equals space 0.7 space straight A

b)

Step 1: State the equation for lost volts

  • The lost volts are the voltage lost due to internal resistance

l o s t space v o l t s space equals space I r

Step 2: Substitute the values

0.7 space cross times space 0.3 space equals space 0.21 space equals space 0.2 space straight V

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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.