Question

One brand of \(12.0-\mathrm{V}\) automotive battery used to be advertised as providing " 600 cold-cranking amps." Assuming that this is the current the battery supplies if its terminals are shorted, that is, connected to negligible resistance, determine the internal resistance of the battery.

Short answer

Question: Determine the internal resistance of a battery with voltage 12.0 V and advertised cold-cranking amps of 600 A. Answer: The internal resistance of the battery is 0.02 Ω.

Step-by-step solution

Write down the given variables

We are given the following information: - Voltage, V = \(12.0\,\mathrm{V}\) - Cold-cranking current, I = \(600\,\mathrm{A}\)

Use Ohm's Law to find the internal resistance

As mentioned in the analysis, we will use Ohm's Law to determine the internal resistance (r): \(V = I \times r\) Now, we need to find the internal resistance (r): \(r = \frac{V}{I}\)

Substitute the given values and solve for internal resistance

Now, substitute the given values for V and I into the equation from Step 2: \(r = \frac{12.0\,\mathrm{V}}{600\,\mathrm{A}}\) \(r = \frac{12.0}{600}\) \(r = 0.02\,\mathrm{\Omega}\)

State the final answer

The internal resistance of the battery is \(0.02\,\mathrm{\Omega}\).

Key concepts

Ohm's Law

Ohm's Law is a fundamental principle in the world of electronics and electrical engineering. It describes the relationship between voltage (V), current (I), and resistance (R) in an electric circuit. The law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant. The formula to express Ohm's Law is:
\[ I = \frac{V}{R} \]
This formula can be rearranged to solve for voltage or resistance if the other two quantities are known. Ohm's Law is crucial for understanding how to control the flow of electric current in a circuit.
When applying Ohm's Law to determine the internal resistance of a battery, as in the exercise, we consider the battery's voltage and the current produced when its terminals are shorted through a negligibly small external resistance. This internal resistance can limit the battery's performance, especially in high-demand applications like cold-cranking an engine, where large currents are required.

Electric Circuits

Electric circuits are pathways through which electric current flows. They are composed of various electrical elements like resistors, capacitors, inductors, and power sources like batteries. The configuration of these elements—series or parallel—affects the overall resistance and current flow in the circuit.
In the context of the given exercise, we consider a very simple circuit: a battery with an internal resistance and virtually no external resistance ('short circuit'). Even in this bare-bones configuration, principles such as Ohm's Law still apply. When a battery is short-circuited, the electric current seeks the path of least resistance, which ideally is outside the battery, but due to the internal resistance, the battery will not provide infinite current. This demonstrates that every electrical component, including power sources, influences the characteristics of an electric circuit.

Current and Voltage

Current and voltage are two foundational concepts in electricity. Current, measured in amperes (A), is the rate at which electric charge flows through a point in a circuit. Voltage, measured in volts (V), is the difference in electric potential between two points in a circuit. It's the 'pressure' that drives electric charge to flow, resulting in current.
In our exercise scenario, the automotive battery's potential difference is 12.0 volts and is capable of supplying 600 amps to the circuit when shorted. The voltage is the 'energy' per charge that the battery can provide, while the current is how much charge flows per unit time. Understanding the relationship between current and voltage is critical in analyzing and designing electronic devices and circuits, ensuring they operate safely and effectively. Moreover, these concepts help to understand the power capacity of the battery, which can be calculated as the product of voltage and current, indicating how much work the battery can do at a given time.