A metallic coil is connected in the left gap of a meter bridge and a standard fixed resistor is connected in the right gap. When the coil is kept in an ice bath at 0^ C , the balance point is found to be 25 cm from the left end. When the coil is immersed in boiling water at 100^ C , the balance point shifts to 50 cm from the left end. If the temperature coefficient of resistance of the coil is x 10⁻³ ^ C ⁻¹ , the val

Step-by-step solution

Let the resistance of the coil at 0^ C be R₀ and at 100^ C be R₁₀₀ . Let the fixed resistance in the right gap be R . At 0^ C , the balance point is 25 cm . Using the meter bridge principle: R₀ R = 25 100 - 25 = 25 75 = 1 3 (1) At 100^ C , the balance point is 50 cm : R₁₀₀ R = 50 100 - 50 = 50 50 = 1 (2) Dividing equation (2) by equation (1): R₁₀₀ R₀ = 1 1 3 = 3 The variation of resistance with temperature is given by: R₁₀₀ = R₀(1 + T) R₁₀₀ R₀ = 1 + (100 - 0) 3 = 1 + 100 100 = 2 = 0.02 ^ C ⁻¹ = 20 10⁻³ ^ C ⁻¹ Compa