Skip to content
dronacharya.ai
← JEE Advanced 2020 · Paper 2
PhysicsNumerical+4Question 14 of 54

JEE Advanced 2020 · Paper 2, Physics question 14

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 R3R_3 has temperature coefficient 0.0004 ∘C−10.0004\ ^\circ\mathrm{C}^{-1}. If the temperature of R3R_3 is increased by 100 ∘100\ ^\circC, the voltage developed between SS and TT will be ______ volt.

Wheatstone bridge: R₁ = 60 Ω (S to P) and R₂ = 100 Ω (P to T) on top; R₃ = 300 Ω (S to Q) and R₄ = 500 Ω (Q to T) below. A 50 V battery is connected between P and Q, and a voltmeter V between S and T.
Answer and worked solution

Official answer: 0.26

Balance check. 60100=300500\frac{60}{100}=\frac{300}{500}, so the bridge is balanced. The battery is across P and Q, and each branch acts as a potential divider. Take VQ=0V_Q=0, VP=50V_P=50 V.

After heating.
R3=300(1+0.0004×100)=312 Ω.R_3=300(1+0.0004\times100)=312\ \Omega.

Potentials.
VS=50⋅31260+312=41.94 V,VT=50⋅500100+500=41.67 V.V_S=50\cdot\frac{312}{60+312}=41.94\text{ V},\qquad V_T=50\cdot\frac{500}{100+500}=41.67\text{ V}.

VS−VT≈0.27 V.V_S-V_T\approx0.27\text{ V}.
Answer: 0.27 (key: 0.26 to 0.28)

Topics:Wheatstone bridge and metre bridgeTemperature dependence of resistance
← Previous questionNext question →