A Wheatstone bridge ABCD has four arms with resistances AB = 10 , BC = 10 , AD = 10 , and DC = S , where S is a metallic wire. A galvanometer is connected between B and D , and a battery is connected across A and C . At 0^ C , the bridge is perfectly balanced. When the wire S is heated to a temperature T^ C , the bridge becomes unbalanced. To restore the balance, a 40 resistor is connected in parallel with the arm AB

Step-by-step solution

For the Wheatstone bridge to be balanced, the ratio of resistances must satisfy: R_ AB R_ BC = R_ AD R_ DC At 0^ C , the bridge is balanced with S in arm DC . Let its resistance be S₀ : 10 10 = 10 S₀ S₀ = 10 At T^ C , the resistance of S becomes S_T . To restore balance, a 40 resistor is connected in parallel with AB . The new resistance of arm AB is: R_ AB ' = 10 40 10 + 40 = 400 50 = 8 Using the balance condition again for the new setup: 8 10 = 10 S_T S_T = 100 8 = 12.5 The temperature dependence of resistance is