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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: 9780137488179Not the one you use?Change textbook
Chapter 24, Problem 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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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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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Related Practice
Textbook Question

The level of liquid helium (temperature ≈ 4K) in its storage tank can be monitored using a vertically aligned niobium–titanium (NbTi) wire, whose length ℓ spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current I at all times in the NbTi wire and a voltmeter monitors the voltage V across this wire. The NbTi wire is superconducting ( R = 0) if below its transition temperature of 10 K, so the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define ƒ = x/ℓ to be the fraction of the tank filled with liquid helium (Fig. 25–40) and V₀ to be the value of the voltage V when the tank is empty (ƒ = 0) . Determine the relation between f and V (in terms of V₀).

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Textbook Question

A 100-W, 120-V incandescent lightbulb has a resistance of 12 Ω when cold (20°C) and 150 Ω when on (hot). Calculate its power consumption (a) at the instant it is turned on, and (b) after a few moments when it is hot.

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Textbook Question

Household wiring has sometimes used aluminium instead of copper.Typical copper wire used for home wiring in the U.S. has a diameter of 1.63 mm. What is the resistance of 125 m of this wire?

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Textbook Question

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 current through each bulb?

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Textbook Question

Suppose a current is given by the equation I = 1.40 sin 210t, where I is in amperes and t in seconds. What is the rms value of the current?

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Textbook Question

Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1250 W of power total. What power is wasted in 25.0 m of this wire?

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