Question

In the circuit shown in the adjoining figure the current between B and D is zero, the unknown resistance is of:

• A. 3 $ \Omega $
• B. 2 $ \Omega $
• C. 4 $ \Omega $
• D. emf of a cell is required to final the value of X.

Answer 1

Answer: (B)

Equivalent resistance of $ {{R}_{1}} $ and $ {{R}_{2}} $ . $ P={{R}_{1}}+{{R}_{2}}=12+4=16\Omega $ Equivalent resistance of $ {{R}_{3}} $ and $ {{R}_{4}} $ $ Q=1+3=4\Omega $ Equivalent resistance of $ {{R}_{5}} $ and $ {{R}_{6}} $ $ R=\frac{1\times 1}{1+1}=\frac{1}{2}\Omega $ For no current in arm BD, bridge should be balanced. $ \frac{P}{Q}=\frac{R}{S} $ $ \frac{16}{X}=\frac{4}{1/2} $ $ \frac{16}{X}=8 $ $ \Rightarrow $ $ X=2\Omega $