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Ch. 25 - Electric Current and Resistance
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 24, Problema 86b

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications. What is the resistance of each bulb?

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To find the resistance of each bulb, we use the formula derived from Ohm's Law and the power equation: \( P = \frac{V^2}{R} \), where \( P \) is the power, \( V \) is the voltage, and \( R \) is the resistance.
Rearrange the formula to solve for resistance: \( R = \frac{V^2}{P} \).
For Lightbulb A, substitute the given values \( V = 120 \; \text{V} \) and \( P = 40 \; \text{W} \) into the formula: \( R_A = \frac{(120)^2}{40} \).
For Lightbulb B, substitute the given values \( V = 12 \; \text{V} \) and \( P = 40 \; \text{W} \) into the formula: \( R_B = \frac{(12)^2}{40} \).
Simplify the expressions for \( R_A \) and \( R_B \) to find the resistance of each bulb. Ensure the units are consistent and the results are expressed in ohms (\( \Omega \)).

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Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = I * R. This fundamental principle is essential for calculating resistance when voltage and power are known.
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Resistance and Ohm's Law

Power in Electrical Circuits

The power (P) consumed by an electrical device is defined as the rate at which it uses energy, calculated using the formula P = V * I, where V is voltage and I is current. For resistive loads, power can also be expressed as P = V^2 / R or P = I^2 * R, allowing for the determination of resistance when voltage and power ratings are provided.
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Resistance Calculation

Resistance (R) is a measure of the opposition to the flow of electric current in a circuit. It can be calculated using the rearranged power formula R = V^2 / P. By substituting the voltage and power ratings of the lightbulbs into this formula, one can determine the resistance of each bulb, which is crucial for understanding their electrical characteristics.
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Resistivity & Resistors in Circuits
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