Question

A Wheatstone's bridge is balanced with a resistance on \[625\Omega \] in the third arm, where P, Q and S are in the 1st, 2nd and 4th arm respectively. If P and Q are interchanged, the resistance on the third arm has to be increased by \[51\Omega \] to secure balance. The unknown resistance in the fourth arm is

A. \[625\Omega \]
B. \[650\Omega \]
C. \[676\Omega \]
D. \[600\Omega \]

Answer 1

Hint: Wheatstone Bridge is a circuit used to measure an unknown resistance by comparing the known resistance or we can say balancing two legs of a bridge circuit, one leg of which includes the unknown component.

Complete step by step answer:
The Balancing Condition for Wheatstone bridge will be:
\[\dfrac{P}{Q} = \dfrac{S}{R}\]
Now applying the value of S from given question we will get:
\[\dfrac{P}{Q} = \dfrac{{625}}{R}\]---------- [1st Equation]
When P and Q are interchanged with one another, we will get
\[\dfrac{Q}{P} = \dfrac{{676}}{R}\]
The above equation can be also written as
\[\dfrac{P}{Q} = \dfrac{R}{{676}}\]---------- [2nd Equation]
Now, solve both the equations 1 and 2. It helps to find the value of Unknown Resistance
\[\dfrac{P}{Q} = \dfrac{{625}}{R} = \dfrac{R}{{676}}\]
$\implies$ \[{R^2} = \sqrt {422500} \]
$\therefore$ \[R = 650\Omega \]

So, the correct answer is “Option B”.

Note:
The benefit of the Wheatstone bridge is the ability to provide extremely accurate measurements. Also, there is no effect of the resistance of the galvanometer or no consumption of the electric energy because at the null point current does not flow in the arm of the galvanometer. This is the main advantage of Wheatstone bridge. It is an easy and convenient method.
Considerable advantages of Wheatstone Bridge are as follows:
a. The prime benefit of Wheatstone Bridge is that it can be effectively interfaced into different combinations.
b. It allows the measurement of very small changes in the bridge. Even it allows the measurement in m ohms.
Disadvantages of Wheatstone Bridge are as follows:
a. Result is non-linear during the measurement of the value of large resistances.
b. Sometimes you can degrade resistance value based upon applied EMF.