Internal Resistance

1. Definition and Key Concepts

• Internal resistance is the resistance inside a battery or cell that reduces the voltage available to the external circuit.
• It is caused by the materials inside the battery, such as chemicals and metal components.
• Represented by the symbol $r$ (measured in ohms, $Ω).$
• An ideal cell would have zero internal resistance ($$r = 0 Ω$$), but real cells always have some internal resistance.

2. Understanding emf and Terminal Voltage

Electromotive Force $(emf)$

• Emf $(ε)$ is the maximum potential difference a cell can provide when no current flows.
• Measured in volts $(V)$ using a voltmeter when the switch is open.

Terminal Voltage $(V)$

• When a circuit is complete, some energy is lost due to internal resistance.
• The terminal voltage (V) is the voltage across the battery when current is flowing.
• Terminal voltage is always less than emf due to internal resistance.

Formula:

$\text{emf} (\varepsilon) = V + Ir$

Where:

• $ε (emf) =$ Maximum voltage when no current flows $(V)$
• $V =$ Terminal voltage $(V)$
• $I =$ Current $(A)$
• $r =$ Internal resistance $(Ω)$

3. Lost Volts

• The voltage drop due to internal resistance is called lost volts.
• Lost volts $= Ir.$
• The more current flows, the more voltage is lost inside the battery.

4. Practical Observations

• When the switch is open: The voltmeter reads the emf $(ε).$
• When the switch is closed: The voltmeter reads the terminal voltage $(V),$ which is lower than the emf due to internal resistance.

5. Ohmic and Non-Ohmic Conductors (Comparison)

Ohmic Conductors	Non-Ohmic Conductors
Follow Ohm's Law $(V = IR).$	Do not follow Ohm's Law.
Graph is a straight line.	Graph is a curve.
Examples: Resistors, nichrome wire.	Examples: Light bulbs, diodes, transistors.

6. Key Takeaways

• Smaller internal resistance = less energy wasted inside the battery.
• High current = More lost volts (battery drains faster).
• To measure internal resistance, use the voltage drop at different currents.