Concept explainers
Review When a metal rod is heated, its resistance changes both because of a change in resistivity and because of a change in the length of the rod. If a silver rod has a resistance of 2.00 Ω at 22.0°C, what is its resistance when it is heated to 200.0°C? The temperature coefficient for silver is α = 6.1 × 10−3 °C−1, and its coefficient of linear expansion is 18 × 10−6 C−1. Assume that the rod expands in all three dimensions.
Resistance of the silver rod when it is heated to
Answer to Problem 75PQ
Resistance of the silver rod when it is heated to
Explanation of Solution
Given that the initial temperature of the rod is
Write the general expression for the resistance of a conductor.
Here,
Write the expression for the temperature dependence of resistivity.
Here,
Write the expression for the linear thermal expansion of material.
Here,
Write the expression for the cross sectional area of the conductor.
Here,
The linear thermal expansion affects the radius of the conductor in accordance with equation (III). Thus, the cross sectional area at a final temperature
Here,
Use equation (II), (III), and (V) in (I).
Write the expression for the resistance of the conductor, corresponding to an initial temperature
Use equation (VII) in (VI).
Conclusion:
Substitute
Therefore, resistance of the silver rod when it is heated to
Want to see more full solutions like this?
Chapter 28 Solutions
EBK WEBASSIGN FOR KATZ'S PHYSICS FOR SC
- A 10.00-meter long wire cable that is made of copper has a resistance of 0.051 ohms, (a) What is the weight if the wire was made of copper? (b) What is the weight of a 10.00-meter-long wire of the same gauge made of aluminum? (c)What is the resistance of the aluminum wire? The density of copper is 8960 kg/m3 and the density of aluminum is 2760 kg/m3.arrow_forwardPower P0 = I0 V0 is delivered to a resistor of resistance R0. If the resistance is doubled (Rnew = 2R0) while the voltage is adjusted such that the current is constant, what are the ratios (a) Pnew/P0 and (b) Vnew/V0? If, instead, the resistance is held constant while Pnew = 2P0, what are the ratios (c) Vnew/V0, and (d) Inew/I0?arrow_forwardExplain why R=R0(1 + a?T) for the temperature variation of the resistance R of an object is not as accurate as P=P0(1 + a?T) which gives the temperature variation of resistivity P.arrow_forward
- If the terminals of a battery with zero internal resistance are connected across two identical resistors in series, the total power delivered by the battery is 8.00 W. If the same battery is connected across the same resistors in parallel, what is the total power delivered by the battery? (a) 16.0 W (b) 32.0 W (c) 2.00 W (d) 4.00 W (e) none of those answersarrow_forwardA coil of insulated aluminum wire has a resistance of 2.15 Q at 20°C. What will be the new temperature if its resistance increased to 2.65 where the temperature coefficient is 0.0039/°C ? O76.39°C O 79.63°C O 79.36°C O 76.93°Carrow_forwardA wire 3.00 m long and 0.450 mm2 in cross-sectional area has a resistance of 40.8 Ω at 20.0°C. If its resistance increases to 41.3 Ω at 28.5°C, what is the temperature coefficient of resistivity?(°C)−1arrow_forward
- You are working at a company that manufactures electrical wire. Gold is the most ductile of all metals: it can be stretched into incredibly long, thin wires. The company has developed a new technique that will stretch 1.30 g of gold into a wire of length L = 2.52 km and uniform diameter. Your supervisor gives you the task of determining the resistance of such a wire (in MO) at 20.0°C. (The density of gold is 19.3 x 103 kg/m3.)arrow_forwardThe resistance of a thin silver wire is 1.0 2 at 20°C. The wire is placed in a liquid bath and its resistance rises to 1.2 2. What is the temperature of the bath? a for silver is 3.8× 10¬3 per °C.arrow_forwardAs the temperature of a metal rod varies, so does the resistance and the dimensions of the rod. If a iron rod has a resistance of 2.78 Ω at 20.0°C, determine the resistance of the rod (in Ω) at 120°C by accounting for the changes in both the resistivity and the dimensions of the rod. The coefficient of linear expansion for iron is 4.50 ✕ 10−6 (°C)−1 and the temperature coefficient of resistivity is 4.50 ✕ 10−3 (°C)−1. Ωarrow_forward
- At 20°C, the carbon resistor in an electric circuit connected to a 6.2-V battery has a resistance of 3.0 ✕ 102 Ω. What is the current in the circuit when the temperature of the carbon rises to 76°C?arrow_forwardA given copper wire has a resistance of 5.08 Q at 20.0°C while a tungsten wire of the same diameter has a resistance of 4.71 Q at 20.0°C. At what temperature will the two wires have the same resistance? °C Need Help? Read Itarrow_forwardA metal resistance thermometer has a resistance = 75.0 2 at = 20 °C. The temperature coefficient of resistance of is 5.2x10^-3/0C. The thermometer is immersed in a container with a melting substance, at which point increases to 120.0 S. What is the melting point of the metal? O a 106.05 °C 149.49 °C 135.38 °C 118,61 °C O e 141.07 °C Of 132,99 °C g 99.49 °C 146.05 °C 139.49 °C 177.97 °C k 154.92 °C 142.50 °C 189.49 °C 92.99 °C 114.92 °C 78.61 °C 102.50 °C Or 137.97 °C 101.17 °C 95.38 °C O O O O 00arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College