PH 106 Midterm: ph106_F08_Exam2_SOLN
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The circuit at right is known as a wheatstone bridge, and it is a useful circuit for measuring small changes in resistance. Three of the four branches on our bridge have identical resistance r, but the fourth has a slightly different resistance, by an amount r such that its total resistance is r + r. You may assume the voltmeter and voltage source are perfect (drawing no current and having no internal resistance, respectively). Bonus: simplify your expression for r r, i. e. , the change in resistance is small. Show that this results in v r. (worth +20% credit on this question. ) Remember that ideal voltmeters draw no current, so the meter in the center of the bridge doesn"t really do anything. If we label the nodes on the bridge a-d, as shown in the gure at right, the voltmeter simply tells us the potential difference between points d and b,
