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184_notes:examples:week7_wire_dimensions [2017/10/09 15:11] – dmcpadden | 184_notes:examples:week7_wire_dimensions [2021/06/14 23:36] – schram45 | ||
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=====Example: | =====Example: | ||
Suppose you have a simple circuit whose wire changes in thickness. The wire is 8 meters long. The first 2 meters of the wire are 3 mm thick. The next 2 meters are 1 mm thick. The last 4 meters are 3 mm thick. The wire is connected to a 12-Volt battery and current is allowed to flow. You use an ammeter and a voltmeter to find that the current through the first 2 meters of wire is $I_1 = 5 \text{ A}$, and the voltage across the first two meters is $\Delta V_1 = 1 \text{ V}$. In all three segments of the wire, determine the magnitude of the electric field inside and the power transmitted. | Suppose you have a simple circuit whose wire changes in thickness. The wire is 8 meters long. The first 2 meters of the wire are 3 mm thick. The next 2 meters are 1 mm thick. The last 4 meters are 3 mm thick. The wire is connected to a 12-Volt battery and current is allowed to flow. You use an ammeter and a voltmeter to find that the current through the first 2 meters of wire is $I_1 = 5 \text{ A}$, and the voltage across the first two meters is $\Delta V_1 = 1 \text{ V}$. In all three segments of the wire, determine the magnitude of the electric field inside and the power transmitted. | ||
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* We represent the situation with diagram below. We number the segments for simplicity of representing the quantities we are interested in (see above in " | * We represent the situation with diagram below. We number the segments for simplicity of representing the quantities we are interested in (see above in " | ||
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====Solution==== | ====Solution==== | ||
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Now, for segment 2. We can use [[184_notes: | Now, for segment 2. We can use [[184_notes: | ||
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+ | <WRAP TIP> | ||
+ | ===Assumptions==== | ||
+ | In order to do this calculation there are two important assumptions that must be made | ||
+ | * The wires have a circular cross section: This allows us to use the formula for the area of a circle to come up with the correct proportion. | ||
+ | * The wires are made of the same material throughout: There are two terms in the electron current equation that are material propeties and these will cancel out for each segment of wire if they are made of the same material. This allows the electric field to only vary with cross sectional area. | ||
+ | </ | ||
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A simple application of the [[184_notes: | A simple application of the [[184_notes: | ||