Welcome to Internal Resistance!
Ever noticed how your phone or laptop gets warm when you’re using it heavily? Or how a car’s headlights dim slightly just as the engine starts? This happens because of a sneaky little concept called internal resistance. In this chapter, we’re going to peel back the label on a battery and look at what’s happening inside. Don't worry if this seems tricky at first—once you see the "big picture" of energy transfer, it all clicks into place!
1. Prerequisite: E.m.f. vs. P.d.
Before we dive into internal resistance, let’s quickly recap two vital terms. Think of electricity like a delivery service:
1. Electromotive Force (e.m.f.): This is the total energy given to each Coulomb of charge by the source (like a battery). It is measured in Volts (V). Think of this as the "potential" energy the delivery truck has when it leaves the warehouse.
2. Potential Difference (p.d.): This is the energy used up by the components in the circuit (like a bulb). It is also measured in Volts (V). Think of this as the packages delivered to the customers.
2. What is Internal Resistance?
In an ideal world, a 1.5V battery would always give 1.5V to your circuit. But we don't live in an ideal world! Every power source is made of materials (chemicals, wires, plates) that have their own resistance. This is called internal resistance (symbol: \( r \)).
The Analogy: Imagine a shop that sells apples. The shopkeeper has 10 apples (the e.m.f.). However, to get to the front door to sell them to you, the shopkeeper gets hungry and eats 1 apple himself (the internal resistance). You only ever see 9 apples at the counter. Those 9 apples are the terminal p.d.
Did you know? Internal resistance is why batteries get warm! The energy "lost" inside the battery is converted into thermal energy.
Key Terms
• Internal Resistance (\( r \)): The resistance to current flow within the power source itself.
• Terminal p.d. (\( V \)): The actual voltage delivered to the external circuit.
• Lost Volts (\( v \)): The voltage "wasted" inside the battery due to its internal resistance.
Section Summary: Real batteries aren't perfect; they use up a little bit of their own energy just to move charge through themselves.
3. The Master Equations
To solve problems in this chapter, we use the principle of Conservation of Energy. The total energy (e.m.f.) must equal the energy used outside the battery plus the energy used inside the battery.
The basic relationship is:
Total Energy (e.m.f.) = Useful Energy (Terminal p.d.) + Wasted Energy (Lost Volts)
In Physics symbols, this is:
\( E = V + v \)
Since \( V = IR \) (for the external circuit) and \( v = Ir \) (for the internal resistance), we can expand this into the two formulas you need for your OCR exam:
1. \( E = V + Ir \)
2. \( E = I(R + r) \)
Where:
• \( E \) = Electromotive force (V)
• \( V \) = Terminal potential difference (V)
• \( I \) = Current (A)
• \( R \) = Load resistance (the external circuit resistance) (\( \Omega \))
• \( r \) = Internal resistance (\( \Omega \))
Mnemonic Aid: You can remember the first equation as the "EVIL" equation: \( E = V + Ir \). (Though internal resistance isn't actually evil, it does "steal" your voltage!)
4. Determining Internal Resistance Experimentally (PAG3)
OCR expects you to know how to find \( r \) in a lab. You can't just stick an Ohmmeter inside a battery! Instead, we use a graph.
Step-by-Step Procedure:
1. Set up a circuit with a cell, a switch, a variable resistor, and an ammeter in series.
2. Connect a voltmeter in parallel across the terminals of the cell.
3. Vary the resistance of the variable resistor to get several pairs of readings for Current (\( I \)) and Terminal p.d. (\( V \)).
4. Plot a graph of \( V \) on the y-axis and \( I \) on the x-axis.
Analyzing the Graph:
If we rearrange our "EVIL" equation (\( E = V + Ir \)) to match the straight-line equation \( y = mx + c \):
\( V = -rI + E \)
When you look at your graph:
• The Gradient of the line is \( -r \) (the negative of the internal resistance).
• The Y-intercept is \( E \) (the e.m.f. of the cell).
Quick Review Box:
• Why does the line slope downwards? Because as you draw more current (\( I \)), more volts are "lost" inside the battery (\( Ir \)), so the terminal p.d. (\( V \)) drops.
• Gradient = \( -r \)
• Intercept = \( E \)
5. Common Pitfalls to Avoid
1. Confusing \( E \) and \( V \): Remember, \( E \) is a constant for the battery (how much it *can* give). \( V \) changes depending on how much current is flowing. If the circuit is "open" (no current), then \( V = E \).
2. Forgetting Units: Always ensure your current is in Amps (not mA) and resistance is in Ohms before calculating.
3. Misreading the Gradient: On a \( V-I \) graph, the gradient is negative. If your gradient is -1.5, your internal resistance is simply 1.5 \( \Omega \). Resistance is never negative!
Chapter Takeaways
• Internal resistance (\( r \)) exists because power sources aren't perfect conductors.
• Lost volts (\( Ir \)) is the energy wasted inside the source.
• The terminal p.d. (\( V \)) is always less than the e.m.f. (\( E \)) when current is flowing.
• You can find \( E \) and \( r \) by plotting a \( V-I \) graph.