Answer

Verified

62.4k+ views

**Hint**The value of the $R$ can be determined by using the resistance balance equation of the wheatstone bridge. The resistance ${R_2}$ is taken as the sum of the $R$ and the other resistance which is given in the diagram, then the resistance $R$ can be determined.

**Useful formula**

The resistance equation of the wheat stone bridge is given by,

$\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{{{R_3}}}{{{R_4}}}$

Where, ${R_1}$, ${R_2}$, ${R_3}$ and ${R_4}$ are the resistance of the individual resistors.

**Complete step by step solution**

From the diagram it is given that,

The resistance of the first resistor is given as, ${R_1} = 5\,\Omega $,

The resistance of the second resistor is given as, ${R_2} = \left( {R + 12} \right)\,\Omega $,

The resistance of the third resistor is given as, ${R_3} = 15\,\Omega $,

The resistance of the fourth resistor is given as, ${R_4} = 60\,\Omega $.

Now,

The resistance equation of the wheat stone bridge is given by,

$\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{{{R_3}}}{{{R_4}}}\,................\left( 1 \right)$

By substituting the resistance values of the first resistor, second resistor, third resistor and fourth resistor in the above equation (1), then the above equation (1) is written as,

$\dfrac{5}{{\left( {R + 12} \right)}} = \dfrac{{15}}{{60}}$

By rearranging the terms in the above equation or cross multiplying the terms in the above equation, then the above equation is written as,

$5 \times 60 = 15 \times \left( {R + 12} \right)$

By multiplying the terms in the LHS in the above equation, then the above equation is written as,

$300 = 15 \times \left( {R + 12} \right)$

By rearranging the terms in the above equation, then the above equation is written as,

$\dfrac{{300}}{{15}} = \left( {R + 12} \right)$

By dividing the terms in the above equation, then the above equation is written as,

$20 = R + 12$

By keeping the term $R$ in one side and the other terms in the other side, then the above equation is written as,

$20 - 12 = R$

By subtracting the terms in the above equation, then the above equation is written as,

$R = 8\,\Omega $

**Hence, the option (A) is the correct answer.**

**Note**The balancing equation of the wheat stone bridge is completely depending on the resistance of the wheatstone bridge. The name for the resistance is given in the direction of the clockwise direction, during this calculation, the naming of the resistance is the most important.

Recently Updated Pages

Write a composition in approximately 450 500 words class 10 english JEE_Main

Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main

What is the common property of the oxides CONO and class 10 chemistry JEE_Main

What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main

If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main

The area of square inscribed in a circle of diameter class 10 maths JEE_Main

Other Pages

Find the magnetic field at P due to arrangement as class 12 physics JEE_Main

Two blocks are in contact on a frictionless table One class 11 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main