On your first day at work as an electrical technician, you...

On your first day at work as an electrical technician, you are asked to determine the resistance per meter of a long piece of wire. The company you work for is poorly equipped. You find a battery, a voltmeter, and an ammeter, but no meter for directly measuring resistance (an ohmmeter). You put the leads from the voltmeter across the terminals of the battery, and the meter reads $12.9 \mathrm{~V}$. You cut off a $20.0 \mathrm{~m}$ length of wire and connect it to the battery, with an ammeter in series with it to measure the current in the wire. The ammeter reads $6.90 \mathrm{~A}$. You then cut off a $40.0 \mathrm{~m}$ length of wire and connect it to the battery, again with the ammeter in series to measure the current. The ammeter reads $4.20 \mathrm{~A}$. Even though the equipment you have available to you is limited, your boss assures you of its high quality: The ammeter has very small resistance, and the voltmeter has very large resistance. What is the resistance of 1 meter of wire?

Key Concepts

Ohm's Law

Ohm's Law is the fundamental principle that relates voltage, current, and resistance in an electrical circuit through the equation V = IR. It is widely used to calculate one of these three quantities when the other two are known and forms the basis for analyzing many types of circuits.

Internal Resistance

Internal resistance refers to the resistance that is inherent within a power source, such as a battery, causing a drop in the terminal voltage when current is drawn. Accounting for internal resistance is vital when precise calculations are needed, especially when the measured voltage across the load is affected by the source's own resistance.

Series Circuit Analysis

Series circuit analysis involves examining circuits where components are connected one after the other, ensuring the same current flows through each component. The total resistance in a series circuit is the sum of the individual resistances, which aids in determining unknown resistances when additional known resistances are present or when the circuit includes elements like internal resistance of a battery.

Resistance Measurement Techniques

Resistance measurement techniques often rely on indirect methods when direct measurement tools like an ohmmeter are not available. By measuring voltage and current and applying Ohm's Law, one can infer the resistance of a component. This method is particularly useful in practical scenarios where only a battery, an ammeter, and a voltmeter are available.

Instrument Characteristics

Understanding the characteristics of measuring instruments is critical for circuit analysis. A voltmeter with very high resistance minimizes the current drawn from the circuit, while an ammeter with very low resistance does not appreciably alter the current it measures. This knowledge ensures that the measurements accurately reflect the circuit's true behavior without significant interference.

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