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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 90a

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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Determine the resistance of the copper wire using the formula for resistance: R=ρL where R is resistance, rho is resistivity of copper, and l is length of wire.
Calculate the power loss using the formula for power dissipation in a resistor: p= i r

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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. This relationship is expressed as V = IR, where V is voltage, I is current, and R is resistance. Understanding this law is crucial for calculating the current flowing through the copper wire when connected to the appliances.
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Resistance of a Wire

The resistance of a wire is determined by its material, length, and cross-sectional area. For a cylindrical wire, resistance (R) can be calculated using the formula R = ρ(L/A), where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area. In this case, knowing the diameter of the copper wire allows us to calculate its resistance, which is essential for determining the power loss due to resistance.
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Power Loss in Electrical Circuits

Power loss in electrical circuits, often referred to as resistive or I²R loss, occurs when current flows through a resistance, resulting in energy being dissipated as heat. The power loss (P_loss) can be calculated using the formula P_loss = I²R, where I is the current and R is the resistance. This concept is vital for determining how much power is wasted in the copper wire when the appliances are operating.
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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 resistance of each bulb?

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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

Household wiring has sometimes used aluminium instead of copper. What would be the resistance of the same wire if it were made of aluminum?

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