Given below is an arrangement of resistors in the form of a Wheatstone Bridge. Find the value of x so that the galvanometer holds zero reading.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2\,\Omega \)
The galvanometer reads zero when the bridge is balanced, that is when the ratio of the resistances in the two upper arms equals the ratio in the two lower arms.
\( \displaystyle \frac{P}{Q} = \frac{R}{S} \)
Readings from the figure (the galvanometer joins the top and bottom junctions):
\( P = 12 + 4 = 16\,\Omega\ \text{(series)} \)
\( Q = x \)
\( R = 1 + 3 = 4\,\Omega\ \text{(series)} \)
\( \displaystyle S = \frac{1 \times 1}{1 + 1} = 0.5\,\Omega\ \text{(two}\ 1\,\Omega\ \text{in parallel)} \)
Putting these in the balance condition:
\( \displaystyle \frac{16}{x} = \frac{4}{0.5} = 8 \)
\( \displaystyle x = \frac{16}{8} = 2\,\Omega \)