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Electric circuits Internal resistance Intro: PHYSICS grade 11 and 12
Miss Martins Maths and Science
Overview
This video introduces the concept of internal resistance in electric circuits, a factor previously ignored in introductory physics. It explains that every battery has an inherent internal resistance which causes a voltage drop within the battery itself, meaning the battery cannot supply its full electromotive force (emf) to the external circuit when current is flowing. The video demonstrates this using a simulation, showing how the terminal voltage decreases when a circuit is closed compared to when it's open. It also derives and explains the key formula relating emf, current, external resistance, and internal resistance.
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Chapters
- Previously, introductory circuit analysis ignored the internal resistance of batteries and the resistance of connecting wires.
- From this point onward, the internal resistance of the battery must be considered.
- Internal resistance (represented by 'r') is a property of the battery itself, causing some energy to be consumed within the battery.
- This means a battery's voltage output to the external circuit is less than its maximum possible output (emf) when current flows.
Understanding internal resistance is crucial because it explains why real-world batteries don't deliver their full rated voltage to devices, impacting circuit performance and calculations.
A 5-volt battery cannot supply 5 joules of energy per coulomb to the external circuit because some of that energy is used internally due to its resistance.
- Electromotive force (emf) is the maximum energy per unit charge a battery can provide, measured when no current is flowing.
- When a voltmeter is connected across a battery's terminals with the switch open (no current), it reads the emf.
- When a circuit is closed and current flows, the voltage measured across the battery terminals is the terminal potential difference (V_external or V_load).
- The terminal voltage is always less than the emf when current is flowing.
Distinguishing between emf and terminal voltage is essential for accurately calculating voltage available to the external circuit and understanding energy losses.
In a simulation, a battery with a 9V emf reads 9V on a voltmeter when the switch is open, but drops to 8.18V when the switch is closed and current flows.
- The difference between the emf and the terminal voltage is called 'lost volts' or internal voltage drop (V_internal).
- This voltage drop occurs because the battery's internal resistance opposes the flow of charge within the battery itself.
- The energy associated with lost volts is converted into heat within the battery.
- V_internal can be calculated as the product of the total current (I) and the internal resistance (r).
Identifying 'lost volts' quantifies the energy dissipated within the battery, helping to understand efficiency and potential heating issues.
If a battery's emf is 1.5V and its terminal voltage is 1.2V when current flows, the lost volts (V_internal) are 0.3V.
- The relationship between emf, current, and resistances can be expressed by a key formula: emf = I * (R_external + r).
- This formula combines Ohm's Law for the external circuit (V_external = I * R_external) and the internal circuit (V_internal = I * r).
- The total current (I) is the same throughout the entire circuit, flowing through both the external resistance (R) and the internal resistance (r).
- Rearranging the formula, emf = V_external + V_internal.
This equation provides a powerful tool for solving circuit problems involving internal resistance, allowing prediction of current, voltage drops, and power dissipation.
The formula emf = I * (R_external + r) allows calculation of the total current flowing in a circuit given the battery's emf and the values of external and internal resistance.
Key takeaways
- Internal resistance is an inherent property of all batteries that causes a voltage drop within the battery itself.
- EMF represents the maximum potential energy per unit charge a battery can supply, measured when no current is drawn.
- Terminal voltage is the actual voltage supplied to the external circuit when current is flowing, and it is always less than the EMF.
- The difference between EMF and terminal voltage is known as 'lost volts' or internal voltage drop, caused by current flowing through the internal resistance.
- The total current in a circuit is consistent and flows through both external and internal resistances.
- The fundamental equation emf = I * (R_external + r) links all key circuit parameters when internal resistance is considered.
Key terms
Internal Resistance (r)Electromotive Force (emf)Terminal Potential DifferenceLost VoltsV_externalV_internalTotal Current (I)External Resistance (R_external)
Test your understanding
- What is internal resistance and why was it ignored in earlier circuit studies?
- How does the terminal voltage of a battery change when current starts flowing through it?
- What is the relationship between emf, terminal voltage, and lost volts?
- How can the fundamental equation emf = I * (R_external + r) be used to solve circuit problems?
- Why does a battery's terminal voltage drop when it is connected to an active circuit?