In the situation shown, what is the value of resistance connected between A and D in addition to 12Ω resistance, so that galvanometer shows no deflection?
Please give a detailed answer
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Answers
Given : Wheatstone bridge
To Find : value of resistance connected between A and D in addition to 12Ω resistance, so that galvanometer shows no deflection
Solution:
Let say Effective resistance between A and D is R
To have no deflection in galvanometer hence no current between C and D
10/R = 50/20
=> R = 4 Ω
Let say resistance connected between A and D is x Ω
Added resistance will be in parallel to 12 Ω
Hence 1/R = 1/12 + 1/x
=> 1/4 = 1/12 + 1/x
=> 1/x = 1/4 - 1/12
=> 1/x = ( 3 - 1)/12
=> 1/x = 2/12
=> 1/x = 1/6
=> x = 6
Hence value of resistance connected between A and D in addition to 12Ω resistance is 6 Ω
Correct option is 2) 6 Ω
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