Internal resistance (r) is the resistance inside a real battery or power source itself, which causes the terminal voltage to drop below the EMF whenever current flows, following V = ε − Ir.
Every real battery has stuff inside it (chemicals, electrodes, connections) that resists the flow of charge. We model this as a small resistor r sitting in series with an ideal EMF source, all hidden inside the battery casing. You can't see it or remove it. It's part of the battery.
The consequence is the equation you'll actually use on the exam. The voltage you measure across the battery's terminals is V = ε − Ir, where ε is the EMF (the battery's 'full strength' voltage) and I is the current being drawn. With no current flowing, the terminal voltage equals the EMF. The moment current flows, some voltage gets 'used up' inside the battery, so the circuit only gets what's left over. More current means a bigger internal drop. This is why a car battery's voltage sags when you crank the starter. On the AP exam, the phrase 'ideal battery' is code for r = 0, meaning terminal voltage and EMF are the same thing.
Internal resistance lives in Topic 4.2 (Resistivity and Resistance) in Unit 4 of AP Physics 2, and it's the bridge between idealized circuit diagrams and real lab equipment. The CED expects you to analyze circuits with non-ideal components, and internal resistance is the classic example. It also shows up constantly in experimental design questions. If you plot terminal voltage vs. current for a real battery, you get a straight line with a y-intercept of ε and a slope of −r. That graph is one of the most-loved setups in AP circuit FRQs, because it tests whether you understand that a battery is a model, not a magic constant-voltage box.
Keep studying AP Physics 2 Unit 4
Electromotive Force (EMF) (Unit 4)
EMF and internal resistance are a package deal. EMF is the energy per charge the battery provides, and internal resistance is the tax it charges to deliver it. The terminal voltage equation V = ε − Ir ties them together, and you can't fully define one without the other.
Voltage Drop (Unit 4)
The Ir term in V = ε − Ir is literally a voltage drop, just one that happens inside the battery instead of across an external resistor. Kirchhoff's loop rule treats it exactly like any other resistor's drop, so include it when you walk around a loop.
Ohm's Law (Unit 4)
Internal resistance obeys Ohm's law like any other resistance. The total current in a simple circuit is I = ε / (R + r), which is just Ohm's law applied to the whole loop with the internal and external resistances added in series.
Power Dissipation (Unit 4)
Internal resistance wastes energy as heat inside the battery at a rate P = I²r. This is why batteries get warm under heavy load, and why the power actually delivered to the circuit is always less than the total power εI the EMF source generates.
Internal resistance shows up in two main flavors. In multiple choice, expect a battery with stated EMF and internal resistance, and you'll compute terminal voltage, current, or power, or predict how terminal voltage changes as the load changes. In FRQs, it's usually about non-ideal equipment and lab design. The 2019 exam gave a circuit with a non-ideal ammeter and voltmeters and asked which measurement setup gave better data, which requires understanding how resistance inside a device skews readings. The 2024 long FRQ specified an 'ideal battery of emf ε,' and recognizing that 'ideal' means zero internal resistance tells you terminal voltage equals EMF. A classic experimental task asks you to graph terminal voltage vs. current and extract ε from the intercept and r from the slope. Practice writing that interpretation in a clear sentence, because that's exactly the kind of reasoning the lab-based FRQs reward.
EMF is the battery's maximum, no-load voltage, the energy per unit charge the chemical reaction supplies. Terminal voltage is what the circuit actually receives, and internal resistance is why those two numbers differ. Students often plug EMF into Ohm's law for the external circuit when they should use terminal voltage. Remember V = ε − Ir, so EMF and terminal voltage are only equal when no current flows or when the battery is ideal (r = 0).
Internal resistance is modeled as a small resistor in series with an ideal EMF source, hidden inside the battery.
Terminal voltage follows V = ε − Ir, so it drops below the EMF whenever the battery delivers current.
When a question says 'ideal battery,' that means internal resistance is zero and terminal voltage equals EMF.
On a graph of terminal voltage vs. current, the y-intercept gives the EMF and the slope gives negative the internal resistance.
Internal resistance dissipates power as heat inside the battery at a rate P = I²r, reducing the power delivered to the external circuit.
The total current in a simple loop is I = ε / (R + r), treating internal resistance as just another series resistor.
Internal resistance is the resistance inside a real battery or power source, modeled as a small resistor in series with the EMF. It makes the terminal voltage V = ε − Ir less than the EMF whenever current flows.
Only in two cases. They're equal when no current flows (an open circuit) or when the battery is ideal with zero internal resistance. Otherwise terminal voltage is always less than EMF by the amount Ir.
External resistance comes from components you add to the circuit, while internal resistance is built into the power source itself and can't be removed. Mathematically they behave the same way, so the total current is I = ε / (R + r) with both in series.
Plot terminal voltage on the y-axis against current on the x-axis. Since V = ε − Ir, the y-intercept equals the EMF and the slope equals −r, so the internal resistance is the magnitude of the slope. This graphing setup is a favorite in AP Physics 2 lab-style FRQs.
Yes. Current flowing through the internal resistance dissipates power as heat inside the battery at a rate P = I²r. That's energy the external circuit never gets, and it's why batteries warm up under heavy loads.
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