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Wheatstone Bridge and Its Applications

Wheatstone bridge is an arrangement of four resistances P, Q, R and S connected as shown in the figure. Their values are so adjusted that the galvanometer G shows no deflection. The bridge is then said to be balanced when this condition is achieved. In the setup shown here, the points B and D are at the same potential and it can be shown that\[\frac{P}{Q}=\frac{R}{S}\].

This is called the balancing condition. If any three resistances are known the fourth can be found.

The practical form of wheatstone bridge is slide wire bridge or meter bridge. Using this the unknown resistance can be determined as \[S=\left( \frac{100-l}{l} \right)\times R\] where l is the balancing length of the Meter bridge.

In a wheatstone bridge circuit, \[P=5\Omega \], \[Q=6\Omega \], \[R=10\,\Omega \] and \[S=5\Omega \]. What is the value of additional resistance to be used in series with S, so that the bridge is balanced?

A) \[9\,\Omega \]

B) \[7\,\Omega \]

C) \[10\,\Omega \]

D) \[5\,\Omega \]