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 $R_{3}$ has temperature coefficient $0.0004 ° C^{- 1} .$ If the temperature of $R_{3}$ is increased by $100 ° C$ , the voltage developed between $S$ and $T$ will be _______ volt. [2020]

Question

Smart Achievers · Accepted Answer

(0.27)

According to question, resistance $R_{3}$ has temperature coefficient, $α = 0.0004 ° C^{- 1}$

And temperature is increased by $100 ° C$ i.e., $Δ T = 100 ° C$

$R_{3}' = R_{0} (1 + α Δ T) = 300 (1 + α Δ T)$

$∴$ $R_{3}' = 312 Ω$

$Here, I_{1} = \frac{V}{R_{1} + R_{3}} = \frac{50}{372}$ $and I_{2} = \frac{V}{R_{2} + R_{4}} = \frac{50}{600}$

$V_{S} - V_{T} = 312 I_{1} - 500 I_{2}$

$= 312 (\frac{50}{372}) - 500 (\frac{50}{600})$ $= 41.94 - 41.67 = 0.27 V$

$∴$ $Voltage developed between S and T = 0.27 Volt$

Solution

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