A \(6.0-\mathrm{V}\) battery has internal resistance \(2.5 \Omega .\) If the battery is short-circuited, what's the rate of energy dissipation in its internal resistance?

Ohm's law is fundamental to understanding electric circuits. It is a mathematical equation that describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. The formula is expressed as:
\( V = I \times R \).
This means that the voltage across a conductor is directly proportional to the current flowing through it, provided that the temperature remains constant.

Application in Calculating Current

In our exercise, Ohm's law was used to determine the current flowing through the battery's internal resistance. With a known voltage of 6.0V and internal resistance of 2.5 Ohms, the current was calculated by rearranging Ohm's law to \( I = \frac{V}{R} \), which then yielded a result of 2.4A.
It is important for students to grasp Ohm's law as it lays the groundwork for analyzing simple to complex circuits and is used extensively in electrical engineering and physics.

Internal resistance is an inherent characteristic of batteries, dictating that no battery is a perfect provider of electric energy. This resistance is caused by the materials within the battery that inhibit the flow of electrons, and thus, reduces the efficiency of the battery.

Effect on Energy Dissipation

When you short-circuit a battery, like in our problem, the current does not encounter any external resistance, and all the current must flow through the battery's internal resistance. As a result, this leads to energy dissipation within the battery itself in the form of heat. The formula for power, related to internal resistance, is \( P = I^2 \times R \), demonstrating how the current squared, multiplied by the internal resistance, shows the rate of energy being dissipated. The concept of internal resistance is crucial when considering the battery's performance and efficiency, especially in high-demand applications.

Power in electrical circuits represents the rate at which energy is used or dissipated. It is measured in watts (W) and is calculated using the formula:
\( P = I^2 \times R \), where P is the power, I is the current, and R is the resistance. This equation tells us that power is proportional to the square of the current multiplied by the resistance in the circuit.

Interpreting the Formula

Understanding this power formula is essential, as it can demonstrate how varying either the current or the resistance will impact the total energy dissipation rate. When dealing with direct current (DC) circuits, like in the short-circuited battery of our exercise, power calculation becomes straightforward, which yielded a result of 14.4 watts. This measurement of power explains the energy transformation from electrical to heat within the battery and is an important concept for students to understand how electrical energy is managed in circuits.