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IB DP Physics 2025 SL Study Notes

2.5.7 Electric Cells, Emf, and Internal Resistance

IB Syllabus focus:

  • 'Understanding the characteristics of electric cells, including their electromotive force (emf) and internal resistance.

  • Applying the formula for total emf:
    ε = I (R + r)
    where ε is the emf, I is the current, R is the external resistance, and r is the internal resistance.

  • Discussing the effects of internal resistance on the performance of electric cells and the overall circuit.'

Characteristics of Electric Cells

Electric cells are unique in their function, offering a source of energy conversion that is indispensable in powering electrical circuits. Their characteristics are profoundly defined by the two core attributes: electromotive force (emf) and internal resistance.

Diagram of an Electric cell circuit showing electromotive force (EMF) and internal resistance (r)

Electric Cell Circuitshowing electromotive force (EMF) and internal resistance (r)

Image Courtesy Testbook

Electromotive Force (emf)

Emf is central to the operation of electric cells. It's the energy supplied by a cell or battery per coulomb of charge passing through it, indicative of the cell’s ability to drive electric current through a circuit.

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Practice Questions

FAQ

Materials used in electric cells are pivotal in determining the internal resistance. Low internal resistance is often associated with cells made using highly conductive materials and efficient electrolytes. For instance, lithium-based cells are renowned for their low internal resistance, attributed to the conductive nature of lithium and its compounds. The design of the cell, including the thickness of the electrodes and the nature of the electrolyte, plays a significant role. A cell with thicker electrodes and a highly conductive electrolyte can often deliver lower internal resistance, leading to higher efficiency and less energy loss within the cell.

Yes, the internal resistance of a cell can be measured directly using a method involving the measurement of the open-circuit voltage and the voltage under load. The open-circuit voltage is the emf of the cell, measured when no current is flowing. The cell is then connected to a known resistance, and the voltage under load is measured. The drop in voltage, the known resistance, and the current flowing (calculated using Ohm’s law) are used to calculate the internal resistance. It's essential to ensure the cell is in a stable condition and not affected by factors like temperature variations during the measurement to get accurate results.

The internal resistance of rechargeable cells significantly affects their charging efficiency. A higher internal resistance means that a considerable portion of the energy being inputted during the charging process is lost as heat. This not only reduces the charging efficiency, making the process longer and less energy-efficient but also can lead to elevated temperatures within the cell. Increased temperatures during charging can potentially affect the lifespan and performance of rechargeable cells. Therefore, cells with lower internal resistance are often preferred for applications where rapid and efficient charging is a critical requirement.

Temperature plays a significant role in influencing the internal resistance of an electric cell. Generally, as the temperature increases, the internal resistance of a chemical cell also tends to increase. This is attributed to the enhanced kinetic energy of the particles within the cell, leading to increased collision frequency and resistance. This rise in internal resistance can lead to a reduction in the cell's efficiency, as more energy is lost as heat. Consequently, the terminal voltage of the cell drops, reducing the effective voltage available to the external circuit. This aspect is critical for applications where consistent performance is paramount, leading engineers to often consider the operating temperature when selecting and designing with electric cells.

Reducing the internal resistance of an existing electric cell is challenging because it is inherently determined by the cell’s materials and construction. However, maintaining optimal operating conditions can mitigate the effects of internal resistance. For instance, operating the cell at an optimal temperature can ensure that the internal resistance does not increase due to temperature extremes. Moreover, the usage of cells in optimal combinations, such as parallel configurations, can effectively reduce the total internal resistance of the battery source, although this doesn’t reduce the internal resistance of individual cells. Proper maintenance and ensuring the cells are adequately charged can also aid in maintaining consistent internal resistance levels.

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