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The top left and right arms of a Wheatstone bridge have resistances P and Q. The bottom left and right arms have resistances R and S. When R = 12 ohm, the bridge is balanced. Now P and Q are interchanged and R = 27 ohm balances the bridge. The resistance S is

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9 ohm

18 ohm

12 ohm

15 ohm

answer is D.

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Detailed Solution

$f o r t h e f i r s t c a s e \frac{P}{Q} = \frac{12}{S} - - - - (1) f o r t h e s e c o n d c a s e \frac{Q}{P} = \frac{27}{S} - - - - (2) m u l t i p l y i n g (1) a n d (2) 1 = \frac{27 x 12}{S^{2}} s o l v i n g S = 18$

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