Four resistors are connected to form a Wheatstone bridge ABCD. The resistances of the arms are R_ AB = 15 , R_ BC = 45 , R_ AD = 20 , and R_ DC = S . The bridge is found to be balanced. The resistor S is made of a wire which has a resistance of 25 at 20^ C and a temperature coefficient of resistance = 0.02 ^ C ⁻¹ . The temperature of the wire S is ____ ^ C .

Step-by-step solution

For a balanced Wheatstone bridge, the ratio of resistances in the arms must satisfy: R_ AB R_ BC = R_ AD R_ DC Substituting the given values: 15 45 = 20 S 1 3 = 20 S S = 60 The resistance of the wire S at temperature T is given by: S = S₀ [1 + (T - T₀)] Substituting the known values ( S₀ = 25 at T₀ = 20^ C ): 60 = 25 [1 + 0.02 (T - 20)] 60 25 = 1 + 0.02 (T - 20) 2.4 = 1 + 0.02 (T - 20) 1.4 = 0.02 (T - 20) T - 20 = 1.4 0.02 = 70 T = 90^ C Answer: 90