You're heading out for spring break, but your car won't start. Your friend says you might have corrosion at the battery terminals-a frequent cause of hard starting because of increased resistance. Having read Example 24.4, you know that the resistance between battery and starter should be around \(1 \mathrm{m} \Omega\). While your friend cranks the starter, you measure \(4.2 \mathrm{V}\) between the battery terminal and the wire carrying current to the starter motor. If the motor draws \(125 \mathrm{A},\) is the resistance in its normal range?

Electrical resistance is a fundamental concept in physics that describes how difficult it is for electric current to flow through a material. It is the hindrance to the flow of electrons which is similar to the way friction impedes motion. When you encounter issues with electronic devices or in this case, a car that won't start, understanding resistance is key.

Materials can be classified based on their ability to conduct electricity: conductors have low resistance, allowing current to pass easily, while insulators have high resistance, restricting electron flow. In the given exercise, a car's battery terminals may have developed corrosion, which increases resistance and prevents the car from starting efficiently. This is because corrosion acts as an insulator.

To measure electrical resistance, one uses the unit Ohm, symbolized by the Greek letter Omega (). A milliohm () is one-thousandth of an Ohm, often used for very low resistances, such as in automotive electrical systems.

The concept of voltage drop is integral for diagnosing electrical problems in circuits. Voltage drop refers to the decrease in electrical potential as current flows through a resistor or a series of resistors. In simpler terms, it's the amount of voltage lost due to resistance in a circuit.

In the exercise, the voltage drop across the corroded battery terminal is measured as ). The ideal situation is a minimal voltage drop, indicating healthy connections and components. A significant voltage drop, on the other hand, signifies excessive resistance which can be due to corrosion or other faults.

When you turn the key in your car's ignition, the battery should efficiently deliver power to start the engine. However, if there's a high resistance due to corrosion, as suspected in the scenario, the voltage drop increases, and the current cannot reach its destination with the required potential, hence the starting issue.

The relationship between current and resistance is at the heart of Ohm's Law, which is fundamental to understanding how electric circuits operate. Ohm's Law states that the current () through a conductor between two points is directly proportional to the voltage () and inversely proportional to the resistance () between them. The formula for Ohm's Law is ).

In the context of the car starting problem, if the resistance is within the normal range, the current required to start the motor flows without significant opposition, and the car starts smoothly. With higher resistance, the current is impeded, leading to starting difficulties. The measured current is ), illustrates the increased resistance due to corrosion. This relationship shows that even a small increase in resistance can result in significant electrical issues. Technicians often use this principle to troubleshoot and ensure all parts of a circuit are functioning optimally for reliable operation.