Differences

This shows you the differences between two versions of the page.

--- 184_notes:examples:week7_wire_dimensions [2017/10/04 00:49] – [Example: Application of Node Rule] tallpaul
+++ 184_notes:examples:week7_wire_dimensions [2017/10/04 13:14] – [Example: Changing the Dimensions of a Wire] tallpaul
@@ Line 1: / Line 1: @@
 =====Example: Changing the Dimensions of a Wire=====
-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 $\Delta V_1 = 1 \text{ V}$.
+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.
-{{ 184_notes:6_nodes.png?300 |Circuit with Nodes}}
 ===Facts===
-  * $I_1=8 \text{ A}$, $I_2=3 \text{ A}$, and $I_3=4 \text{ A}$.
+  * Segment lengths: $L_1=2 \text{ m}$, $L_2=2 \text{ m}$, and $L_3=4 \text{ m}$.
-  * $I_1$, $I_2$, and $I_3$ are directed as pictured.
+  * Segment diameters: $d_1=3 \text{ mm}$, $d_2=1 \text{ mm}$, and $d_3=3 \text{ mm}$.
+  * Current: $I_1 = 5 \text{ A}$.
+  * Voltage: $\Delta V_1 = 1 \text{ V}$, $\Delta V_{battery} = 12 \text{ V}$.
 ===Lacking===
-  * All other currents (including their directions).
+  * Power and electric field in all segments
 ===Approximations & Assumptions===
-  * The current is not changing (circuit is in steady state).
+  * The circuit is in a steady state.
-  * All current in the circuit arises from other currents in the circuit.
+  * Approximating the battery as a mechanical battery.
-  * No resistance in the battery (approximating the battery as a mechanical battery)
+  * The wire has a circular cross-section.
+  * No outside influence on the circuit.
+  * The wire is made of the same material throughout.
 ===Representations===
-  * We represent the situation with diagram given.
+  * We represent the situation with diagram below. We number the segments for simplicity of representing the quantities we are interested in (see above in "Facts").
-  * We represent the Node Rule as $I_{in}=I_{out}$.
+{{ 184_notes:7_wire_dim.png?400 |Circuit Diagram}}
 ====Solution====