The resistance of a heating element is found to be 120 at room temperature which is 20^ C . If the temperature coefficient of the material of the resistor is 1.6 10⁻⁴ C⁻¹ and the resistance is found to be 160 , the temperature of the element is:

Step-by-step solution

The resistance of a conductor at a temperature T is given by the formula R_T = R₀ [1 + (T - T₀)] , where R₀ is the resistance at room temperature T₀ , R_T is the resistance at temperature T , and is the temperature coefficient of resistance. Given values are R₀ = 120 , T₀ = 20^ C , R_T = 160 , and = 1.6 10⁻⁴ C ⁻¹ . Substituting these values into the equation: 160 = 120 [1 + 1.6 10⁻⁴ (T - 20)] Dividing both sides by 120 : 160 120 = 1 + 1.6 10⁻⁴ (T - 20) 4 3 = 1 + 1.6 10⁻⁴ (T - 20) 4 3 - 1 = 1.6 10⁻⁴ (T - 20) 1 3 = 1