The potential difference across the terminals of a battery is 8.40 V when there is a current of

step 1 We have a following situation. So here we have EMF. This is positive and this is negative. R is

The potential difference across the terminals of a battery...

The potential difference across the terminals of a battery is $8.40 \mathrm{~V}$ when there is a current of $1.50 \mathrm{~A}$ in the battery from the negative to the positive terminal. When the current is $3.50 \mathrm{~A}$ in the reverse direction, the potential difference becomes $10.20 \mathrm{~V}$. (a) What is the internal resistance of the battery? (b) What is the emf of the battery?

Key Concepts

Electromotive Force (EMF)

The electromotive force (EMF) is a fundamental concept in circuits that represents the energy per unit charge provided by a power source as it moves electrical charges around a circuit. It is often idealized as the voltage in the absence of any current flow, and it can be thought of as the maximum potential difference the battery can provide, overcoming internal losses such as internal resistance.

Internal Resistance

Internal resistance refers to the inherent resistance found within a real battery or power source due to its materials and chemical processes. This resistance causes a voltage drop within the battery when current flows, reducing the terminal voltage compared to the battery's ideal EMF. It is an important parameter because it impacts the performance and efficiency of the battery, especially under high-current conditions.

Terminal Voltage

Terminal voltage is the effective voltage output measured across the battery's terminals while it is connected in a circuit and delivering current. Unlike the emf, the terminal voltage is affected by the internal resistance of the battery; in a discharge situation it is given by subtracting the voltage drop across the internal resistance from the EMF, while during charging the signs may differ.

Ohm's Law in Electrical Circuits

Ohm's law is a core principle in electrical circuits stating that the voltage across a resistor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance. This principle is applied to analyze battery circuits by modeling the battery as an ideal emf source in series with an internal resistance, allowing the calculation of voltage drops under various loading conditions.

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