Welcome to the World of Internal Resistance!
Ever wondered why your phone gets warm when you're using it heavily, or why the headlights on a car dim slightly just as the engine starts? It’s all down to a sneaky little concept called internal resistance. In our previous lessons, we often treated batteries as "perfect" sources of energy, but in the real world, batteries have their own internal "friction" that we need to account for. Don't worry if this seems a bit abstract at first—once you see the patterns, it’s just like a simple puzzle!
1. The "Perfect" vs. The "Real" Battery
In Physics, we use two main terms to describe the energy in a circuit: e.m.f. and terminal p.d.
Electromotive Force (e.m.f.): This is the total energy per unit charge supplied by the source (like a battery). Think of this as the "theoretical maximum" voltage the battery promises on the label. We use the symbol \( E \).
Internal Resistance: Inside a battery, chemicals are moving and reacting. This physical process isn't 100% efficient. The battery itself resists the flow of charge. We represent this as a tiny resistor inside the battery, using the symbol \( r \).
Terminal Potential Difference (p.d.): This is the actual voltage that makes it out of the battery and into the rest of the circuit (the "load"). We use the symbol \( V \).
The Analogy: The Marathon Runner
Imagine a marathon runner who eats a glucose gel that gives them 100 units of energy (e.m.f.). However, the runner has to use 5 units of energy just to move their own heavy legs and carry their water bottle (internal resistance). Therefore, only 95 units of energy are actually used to move them across the finish line (terminal p.d.).
Key Takeaway: The voltage you actually get (\( V \)) is always a little bit less than the voltage the battery is capable of (\( E \)) whenever a current is flowing.
2. "Lost Volts" – Where did the energy go?
When current flows through the battery, some energy is "wasted" heating up the internal components. This "missing" voltage is called lost volts.
Lost Volts = Current \(\times\) Internal Resistance
\( \text{Lost Volts} = Ir \)
Did you know? This is exactly why your laptop or phone battery feels warm after a long gaming session. The "lost volts" are being converted into thermal energy inside the battery!
Quick Review:
- No current flowing? No lost volts! (Terminal p.d. = e.m.f.)
- High current flowing? Lots of lost volts! (Terminal p.d. drops significantly)
3. The Big Equations
We can put all this together into one simple conservation of energy equation. The total energy (\( E \)) equals the energy used in the circuit (\( V \)) plus the energy wasted inside the battery (\( Ir \)).
Equation 1: \( E = V + Ir \)
(Total energy = Energy used outside + Energy wasted inside)
Since we know from Ohm's Law that the external voltage \( V = IR \) (where \( R \) is the resistance of the actual components like bulbs or motors), we can write:
Equation 2: \( E = I(R + r) \)
(Total e.m.f. = Current \(\times\) Total Resistance)
Common Mistake to Avoid: Don't confuse the big \( R \) with the little \( r \). Big \( R \) is the "load" (the stuff you want to power), and little \( r \) is the "internal" (the battery's own resistance).
4. How to Measure Internal Resistance (PAG 3)
In your lab work, you will likely have to find the internal resistance of a cell yourself. Here is the step-by-step process:
The Setup:
1. Connect a cell in series with an ammeter and a variable resistor (rheostat).
2. Connect a voltmeter in parallel across the terminals of the cell.
3. Change the resistance of the variable resistor to get different values for current (\( I \)) and terminal p.d. (\( V \)).
The Math Trick:
We can rearrange our equation \( E = V + Ir \) into the form of a straight-line graph equation (\( y = mx + c \)):
\( V = -rI + E \)
If you plot Terminal p.d. (\( V \)) on the y-axis and Current (\( I \)) on the x-axis:
- The Gradient of the line will be \( -r \) (negative internal resistance).
- The Y-intercept (where the line hits the vertical axis) will be the e.m.f. (\( E \)).
Memory Aid: Use the mnemonic "VIPER" to remember the graph: V is I times r (with E as the start). Or just remember: The graph goes down because as you draw more current, the battery "loses its breath" and the voltage drops.
5. Summary and Quick Check
Key Terms Summary:
- e.m.f. (\( E \)): Total energy potential (measured in Volts).
- Internal Resistance (\( r \)): The battery's own resistance (measured in Ohms).
- Terminal p.d. (\( V \)): Voltage delivered to the circuit.
- Lost Volts (\( Ir \)): Voltage used up inside the battery.
Quick Self-Test:
If a battery has an e.m.f. of 12V and when you draw a current of 2A, the terminal p.d. drops to 10V, what are the lost volts?
Answer: 12V - 10V = 2V. To find the internal resistance, \( r = \text{Lost Volts} / I = 2V / 2A = 1 \Omega \).
Final Encouragement: Internal resistance is just a way of being honest about how batteries work! If you can handle \( V=IR \), you can handle this. Just treat the internal resistance as one extra little resistor that is always stuck inside the battery box.