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Question

In the circuit shown below, all the resistances are equal, each equal to R. The equivalent resistance between points A and C is
330715_3d5192c19eb9439ab7632741a572cf4c.png
  1. R
  2. 4R
  3. R/2
  4. none of the above

A
R
B
4R
C
none of the above
D
R/2
Solution
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Given: a circuit with resistors, where all resistors have equal resistance i.e., R
To find the equivalent resistance between points A and C
Solution:
The given circuit can be re-written as fig(ii)(as shown above).
Now this circuit is symmetrical about the axis BD. Hence the equivalent circuit becomes as shown in fig(iii). Here resistor on arm ABC the reisitors are in series, similarly in the other arms too. So the circuit will be simplified to fig(iv).
Let the equivalent resistance between points A and C be Req
1Req=12R+12R+12R=32R
Therefore the equivalent resistance between points A and C is 2R3Ω

927122_330715_ans_4e4a9106720f49869052d80013473a33.png

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