Question

The current flowing through a conductor connected across a source is 2A and 1.2 A at 0°C and 100°C respectively. The current flowing through the conductor at 50°C will be ______x10² mA.

Answer 1

Correct Answer: 15

Solution:
Using the formula for the current through the conductor, which relates the current at different temperatures: \[ i_0 R_0 = i_{100} R_{100} \quad \text{[For the same source]} \] This gives: \[ 2 R_0 = 1.2 R_0 [1 + 100\alpha] \quad \Rightarrow \quad 1 + 100\alpha = \frac{5}{3} \quad \Rightarrow \quad 100\alpha = \frac{2}{3} \] Now, calculate \( \alpha \): \[ 50 \alpha = \frac{1}{3} \] Thus, the current at 50°C will be: \[ i_{50} R_{50} = i_0 R_0 \] Substituting values: \[ i_{50} = \frac{i_0 R_0}{R_{50}} = \frac{2 R_0}{R_0 (1 + 50\alpha)} = \frac{2}{1 + \frac{1}{3}} = \frac{2}{\frac{4}{3}} = 1.5 \, \text{A} \] Thus, the current at 50°C is \( 1.5 \, \text{A} = 1500 \, \text{mA} \). Therefore, the correct answer is \( \boxed{1500} \, \text{mA} \).