Six 6.00-V cells, each with an internal resistance of 0.0987...

Six 6.00-V cells, each with an internal resistance of 0.0987 $\Omega$ and current output of $0.658 \mathrm{A},$ are connected in parallel to form a battery in a certain circuit. (a) What is the current in the external circuit? (b) What is the emf of the battery? (c) What is the internal resistance of the battery?

Key Concepts

Equivalent Circuit Analysis

Equivalent circuit analysis involves modeling a battery as an ideal emf source in series with an internal resistance. This simplification enables the application of circuit laws, such as Ohm’s law and Kirchhoff’s voltage law, to calculate various parameters like load current, terminal voltage, and the impact of internal resistance on overall circuit behavior. This approach is fundamental for solving problems where multiple batteries or cells are combined in different configurations.

Electromotive Force (emf)

The emf of a cell represents the ideal voltage provided by the cell when no current flows. It is an inherent property that results from the chemical reactions in the cell and is used to characterize the driving force behind the current in a circuit. In battery analysis, the emf determines the open-circuit voltage and plays a crucial role in determining the performance of the battery in different circuit configurations.

Internal Resistance

Internal resistance is a measure of the opposition to current flow within a cell, caused by its materials and construction. It affects the performance of the battery by causing voltage drops when current is drawn, thereby reducing the effective voltage available to an external circuit. Understanding internal resistance is key in analyzing how much voltage is lost inside the battery, especially when multiple cells are connected together.

Parallel Connection of Cells

When cells are connected in parallel, they share the same voltage across their terminals while the total current supplied to the external circuit is the sum of the individual cell currents. This arrangement can improve the current delivering capacity of the battery and often reduces the overall internal resistance, enhancing the battery's performance in supplying high currents. Analyzing parallel configurations is essential for understanding how current divides among cells and how their internal resistances combine to give an effective resistance.

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