Question

In a Wheatstone bridge all the four arms have equal resistance R. If the resistance of galvanometer arm is also R, the equivalent resistance of combination is
A. 2R
B. R/4
C. R/2
D. R

Answer 1

Hint:This problem is from the section current electricity. The concept of Wheatstone bridge and equivalent resistance are needed to solve this problem.

Formula used:
Equivalent resistance for a series resistance circuit:
${R_S} = {R_1} + {R_2} + {R_3}$
Where ${R_S}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.
Equivalent resistance for a parallel resistance circuit:
$\dfrac{1}{{{R_P}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Where ${R_P}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.

Complete step by step solution:
Since each of the four arms has an equal resistance value R, the Wheatstone bridge circuit is balanced. No current will flow through the galvanometer arm as a result, and its resistance will not function.

The corresponding circuit diagram is shown below. All four resistance have value R.

The equivalent resistance is calculated as,
The two series connection’s equivalence resistance will be ${R_E} = R + R = 2R$. Then
${R_E} = \dfrac{{2R \times 2R}}{{2R + 2R}} = \dfrac{{4R}}{{4R}} = R$

Hence, the correct option is option D.

Additional Information: By balancing the two bridge circuit legs, the Wheatstone bridge determines the unknown resistance. There is an unidentified resistance component in one leg of the Wheatstone bridge. The Wheatstone Bridge Circuit consists of a bridge-shaped connection between two known resistors, one unknown resistor, and one variable resistor. The Wheatstone Bridge is also referred to as the resistance bridge. The Wheatstone bridge operates on the null deflection theory, which states that no current flows across the circuit when the resistance ratios of the two components are equal.

Note: A conductor's electrical resistance is affected by the following parameters: The conductor's cross-sectional area, the conductor's length, the conductor's material and the conducting material's temperature. Electrical resistance is inversely proportional to the cross-sectional area and directly proportional to the conductor's length.