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 k× 10- 2V . Find the value of k. (Approximate the answer to the nearest integer.)

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 k× 10- 2V . Find the value of k. (Approximate the answer to the nearest integer.) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-fppcux8fwlipfzuf.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

R3'=300(.1+α Δ T.) =312 Ω Now <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-fppcux8fwlipdpaa.jpg" /> I1=(50/372) and I2=(50/600) VS-VT=312I1-500I2 =41.94-41.67=0.27 V

R3′​=300(1+αΔT) =312Ω Now I1​=37250​ and I2​=60050​ VS​−VT​=312I1​−500I2​ =41.94−41.67=0.27V

$R_{3}^{^{'}} = 300 (1 + α Δ T)$
$= 312 Ω$
Now

$I_{1} = \frac{50}{372}$ and $I_{2} = \frac{50}{600}$
$V_{S} - V_{T} = 312 I_{1} - 500 I_{2}$
$= 41.94 - 41.67 = 0.27 V$