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
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:
- 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.Determine:
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
Step 3: Substitute the values
b)
Step 1: State the equation for lost volts
- The lost volts are the voltage lost due to internal resistance
Step 2: Substitute the values