In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance R3 has temperature coefficient 0.0004° C -1. If the temperature of R3 is increased by 100 ° C, the voltage developed between S and T will be volt.

Question

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance R3 has temperature coefficient 0.0004° C -1. If the temperature of R3 is increased by 100 ° C, the voltage developed between S and T will be volt. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/dbe93501291a897446832848b9a91a34-.png" /> R 3 prime= R 3(1+α Δ T )=312 Ω V S - V T = I 2 R 2- L 1 R 1 =(50/100+500) × 100-(50/60+312) × 60 ≈ 0.2688 ≈ 0.27 V

R3′​=R3​(1+αΔT)=312Ω VS​−VT​=I2​R2​−L1​R1​ =100+50050​×100−60+31250​×60 ≈0.2688≈0.27V

$R_{3}^{'} = R_{3} (1 + α Δ T) = 312 Ω$
$V_{S} - V_{T} = I_{2} R_{2} - L_{1} R_{1}$
$= \frac{50}{100 + 500} \times 100 - \frac{50}{60 + 312} \times 60$
$\approx 0.2688 \approx 0.27 V$