# HW13-1 - MasteringPhysics 3:55 PM Assignment Display Mode...

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5/10/09 3:55 PM MasteringPhysics Page 1 of 9 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers phy260S09 HW13 Due at 12:00am on Monday, June 1, 2009 View Grading Details Heating a Water Bath Description: Calculate the time required for a resistor to heat a water bath to a given temperature. In the circuit in the figure, a 20-ohm resistor sits inside 111 of pure water that is surrounded by insulating Styrofoam. Part A If the water is initially at temperature 11.6 , how long will it take for its temperature to rise to 59.0 ? Hint A.1 How to approach the problem First reduce the system of resistors to a single equivalent resistor; then use this simplified circuit to calculate the current flowing through the battery. Determine the current flowing through the resistor in the water and calculate its power output. Finally, use the calculated power output to calculate the time needed to heat the water bath. Hint A.2 Calculate the resistance of the circuit Calculate the total resistance of the network of resistors shown in the figure. Hint A.2.1 Reducing a network of resistors to an equivalent resistor For any network of resistors, first look at any section (between two junction points) in which all resistors are in series, and combine them appropriately to obtain the equivalent resistance through that section of the network. Next, see whether any combined sections are in parallel with each other and combine them appropriately to to obtain the equivalent resistance through those sections. Continue this process, alternating between sections in series and sections in parallel, until all the resistors have been combined to make a single equivalent resistor for the system. Hint A.2.2 Combining the resistors in the middle section After the current flows through the resistor in the water bath, it splits into three separate paths, each with two resistors. What is the equivalent resistance through this section? Hint A.2.2.1 Series or parallel? In the middle section there are six resistors. How are they combined in the circuit? ANSWER: All six resistors are in series. All six resistors are in parallel. There are three paths in series and each path consists of two resistors in parallel. There are three paths in parallel and each path consists of two resistors in series. Hint A.2.2.2 Resistance in each path Calculate the resistance of each path, , , , from top to bottom respectively. Express your answers, separated by commas, using three significant figures. ANSWER: , , =

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5/10/09 3:55 PM MasteringPhysics Page 2 of 9 http://session.masteringphysics.com/myct Hint A.2.2.3 Resistors in parallel For resistors connected in parallel, for any number of resistors. Once the three separate paths in the middle section have been reduced to their equivalent resistances, it is evident that the three paths are in parallel.
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