A uniform metallic wire is bent to form a square loop ABCD . A galvanometer is connected between points B and D . When a battery of 10 V is connected across points A and C , the galvanometer shows zero deflection and the total current drawn from the battery is 2 A . The total resistance of the uniform wire before it was bent is:

Step-by-step solution

Zero deflection in the galvanometer indicates that the Wheatstone bridge formed by the square loop is balanced. Let the resistance of each side of the square loop be r . The equivalent resistance R_ eq of the circuit across points A and C is the parallel combination of the branches ABC and ADC . Resistance of branch ABC = r + r = 2r . Resistance of branch ADC = r + r = 2r . R_ eq = 2r 2r 2r + 2r = r . From Ohm's law, the equivalent resistance can also be calculated using the total voltage and current: R_ eq = V I =