(455) Internal resistance [IB Physics SL/HL]

Internal Resistance

• Definition: Internal resistance occurs in real-life circuits as batteries are not ideal; they have their own resistance.

• Analogy: Think of it as some voltage being 'eaten away' by the battery’s internal resistance.

• Visual Representation: A zoomed-in view of a battery can be depicted with an electromotive force (EMF, ε) and internal resistance (r).

Electromotive Force (EMF)

• EMF Definition: Measured in volts, it represents the potential difference a battery tries to deliver (not a force in Newtons).

• Analogy: Imagine a battery trying to give out 10 pieces of chocolate, with internal resistance consuming some (resulting in a lower output).

Key Equation

• The relationship involving EMF, current (I), and resistances in a circuit:[ ε = I(R + r) ]

• This breaks down to:

  • EMF (ε): Battery's output

  • I: Current in amperes

  • R: External resistance

  • r: Internal resistance

Circuit Example

• Example Setup: A circuit with 10 identical 5-ohm resistors in parallel.

• Calculating Equivalent Resistance:

  • Formula: [ 1/R_P = (1/R + 1/R + ... + 1/R) ] for 10 resistors.

  • Result:

    • [ 1/R_P = 10 * (1/5) = 2 ]

    • Therefore, [ R_P = 0.5 \text{ ohms} ]

Solving for Circuit Current

• Given:

  • Internal resistance (r) = 0.1 ohms

  • EMF (ε) = 6 volts

• Finding Circuit Current (I):

  • Formula rearrangement:[ I = \frac{ε}{R + r} ]

  • Calculation:[ I = 6}/{0.5 + 0.1} = {6}/{0.6} = 10 { A} ]

Potential Difference Across Terminals

• To find the potential difference (V) across the battery’s terminals:

  • Formula: [ V = IR ]

  • Using current (I = 10 A) and external resistance (R = 0.5 ohms):[ V = 10 * 0.5 = 5 V]

Conclusion

• The internal resistance and EMF relationship are crucial for understanding real circuit behavior, leading to adjustments in expected voltage outputs.