AP Physics 1 Question 48: Answer and Explanation

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Question: 48


A Wheatstone bridge (diagram above) is a configuration of resistors and a sensitive current meter, called a galvanometer, that is used to determine the resistance of an unknown resistor. In the Wheatstone bridge shown here, find the value of Rx such that the current through galvanometer G is zero.

  • A. 25 Ω
  • B. 15 Ω
  • C. 10 Ω
  • D. 2.5 Ω

Correct Answer: D


D The question specifies that the current through G must be 0. Recall that in parallel circuits current will distribute itself in a manner inversely proportional to the resistance in each path. Looking at the left-hand side of the configuration, we see that the resistance on the top is half the resistance of the bottom. That means the current will distribute itself with 2/3 along the top path and 1/3 along the bottom path. For no current to pass through G, this same distribution must also be true on the right-hand side, otherwise some current would pass through G to correct any changes to the relative resistances. The 5 Ω resistor must have the same proportional resistance to the unknown resistor that the 20 Ω resistor has to the 10 Ω resistor. Therefore, the unknown must be 2.5 Ω.