Differences

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

--- 184_notes:examples:week8_wheatstone [2021/06/29 00:15] – schram45
+++ 184_notes:examples:week8_wheatstone [2021/07/22 18:28] (current) – schram45
@@ Line 57: / Line 57: @@
 [{{ 184_notes:8_wheatstone_current_directions.png?300 |Circuit with Wheatstone bridge, and directed current}}]
-To find  $\Delta V_{\text{light}}$ , we will need to set up some equations using the Loop Rule and Node Rule. We will focus on Nodes C and D, and the Loops highlighted below. Note that if you want to be able to solve for everything in the circuit, you have to use some loop equations and some node equations (you can't use only loop or only nodes).
+To find  $\Delta V_{\text{light}}$ , we will need to set up some equations using the Loop Rule and Node Rule. We will focus on Nodes A and B, and the Loops highlighted below. Note that if you want to be able to solve for everything in the circuit, you have to use some loop equations and some node equations (you can't use only loop or only nodes).
 [{{ 184_notes:8_wheatstone_loops.png?900 |Highlighted loops in Wheatstone bridge circuit}}]
@@ Line 63: / Line 63: @@
 Applying the Node Rule and the Loop Rule, we obtain the following equations:
 \begin{align*}
-  I &= I_1 + I_2 &(\text{Node C}) \\
+  I &= I_1 + I_2 &(\text{Node A}) \\
-  I &= I_3 + I_4 &(\text{Node D}) \\
+  I &= I_3 + I_4 &(\text{Node B}) \\
   \Delta V_{\text{bat}} &= \Delta V_1 + \Delta V_3 &(\text{Loop 1}) \\
   \Delta V_{\text{bat}} &= \Delta V_2 - \Delta V_{\text{light}} + \Delta V_3 &(\text{Loop 2}) \\
@@ Line 81: / Line 81: @@
 Since we know  $\Delta V_3$  and all the resistances, all that remains is to rearrange and solve for  $\Delta V_{\text{light}}$ :
  $\Delta V_{\text{light}} = \frac{\Delta V_3\left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}\right) - \Delta V_{\text{bat}}\left(\frac{1}{R_1} + \frac{1}{R_2}\right)}{\frac{1}{R_2} + \frac{1}{R_4}} = 2.37 \text{ V}$
+Looking at loop 2 alone between the power source and resistor 3 we would expect the voltage across any other elements in that loop to be small. Our answer agrees with this observation as 2.37 is quite small compared to both the battery and resistor 3.