A Wheatstone bridge has four arms with resistances P = 10 , , Q = 20 , , R = 15 , , and S being a metallic coil. The bridge is initially balanced at 20^ C . The temperature of the coil S is then raised to 120^ C . If the temperature coefficient of resistance of the coil's material is 5 10⁻³ , ^ C ⁻¹ , what value of shunt resistance must be connected in parallel with the heated coil to restore the balance of the bridg

Step-by-step solution

For the bridge to be balanced initially, P Q = R S₀ . Substituting the given values: 10 20 = 15 S₀ S₀ = 30 , . When the temperature of the coil is raised, its new resistance S' is given by: S' = S₀(1 + T) S' = 30 [1 + 5 10⁻³ (120 - 20)] S' = 30 [1 + 0.5] = 45 , . To restore the balance, the equivalent resistance of this arm must be brought back to 30 , . Since 45 , > 30 , , a shunt resistance R_x must be connected in parallel. 1 S' + 1 R_x = 1 S₀ 1 45 + 1 R_x = 1 30 1 R_x = 1 30 - 1 45 = 3 - 2 90 = 1 90 R_x = 90 ,