Answered: Problem 1. What is the equivalent…

Problem 1. What is the equivalent resistance of the combination of resistors between points a and b in the figure? Note that one end of the vertical resistor is left free. R R R R R

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter10: Direct-current Circuits

Section: Chapter Questions

Problem 3CQ: Show that the power dissipated by the load resistor is maximum when the resistance of the load...

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An office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20.C to 100. C in 4.00 minutes. The heater is a Nichrome resistance wire connected to a 120-V power supply. Assume the wire is at 100. C throughout the 4.00-min time interval. (a) Calculate the average power required to warm the water to 100. C in 4.00 min. (b) Calculate the required resistance in the heating element at 100. C. (c) Calculate the resistance of the heating element at 20. C. (d) Derive a relationship between the diameter of the wire, the resistivity at 20. C, 0, the resistance at 20. C, R0, and the length L. (e) If L = 3.00 m, what is the diameter of the wire?
When a straight wire is heated, its resistance changes according to the equation R = R0 [1 + (T T0)] (Eq. 17.7), where is the temperature coefficient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is R=R0[1+(TT0)][1+(TT0)][1+2(TT0)] where is the coefficient of linear expansion. (See Topic 10.) (b) Compare the two results for a 2.00-m-long copper wire of radius 0.100 mm, starting at 20.0C and heated to 100.0C.
Integrated Concepts (a) An immersion heater utilizing 120 V can raise the temperature of a 1.00 102 -g aluminum cup containing 350 g of water from 20.0°C to 95.0°C in 2.00 min. Find its resistance, assuming it is constant during the process. (b) A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.
An office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20.C to 100. C in 4.00 minutes. The heater is a Nichrome resistance wire connected to a 120-V power supply. Assume the wire is at 100. C throughout the 4.00-min time interval. (a) Calculate the average power required to warm the water to 100. C in 4.00 min. (b) Calculate the required resistance in the heating element at 100. C. (c) Calculate the resistance of the heating element at 20. C. (d) Derive a relationship between the diameter of the wire, the resistivity at 20. C, 0, the resistance at 20. C, R0, and the length L. (e) If L = 3.00 m, what is the diameter of the wire?
A 120-V immersion heater consists of a coil of wire that is placed in a cup to boil the water. The heater can boil one cup of 20.00°C water in 180.00 seconds. You buy one to use in your dorm room, but you are worried that you will overload the circuit and nip the 15.00-A, 120-V circuit breaker, which supplies your dorm room. In your dorm room, you have four 100.00-W incandescent lamps and a 1500.00-W space heater, (a) What is the power rating of the immersion heater? (b) Will it trip the breaker when everything is turned on? (c) If it you replace the incandescent bulbs with 18.00-W LED, will the breaker nip when everything is turned on?
Construe! Your Own Problem Consider a rechargeable lithium cell that is to be used to power a camcorder. Construct a problem in which you calculate the internal resistance of the cell during normal operation. Also, calculate the minimum voltage output of a battery charger to be used to recharge your lithium cell. Among the things to be considered are the emf and useful terminal voltage of a lithium cell and the current it should be able to supply to a camcorder.
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Show that the power dissipated by the load resistor is maximum when the resistance of the load resistor is equal to the internal resistance of the battery.
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