Resistance and Temperature?

📌 CONCEPT: The resistance of a wire is directly proportional to its temperature, as per the formula for temperature dependence of resistance, which is R = R0(1 + α(T - T0)), where R is the final resistance, R0 is the initial resistance, α is the temperature coefficient of resistance, T is the final temperature, and T0 is the initial temperature.

📐 RULE / FORMULA: The formula for temperature dependence of resistance is R = R0(1 + α(T - T0)).

💡 WORKED EXAMPLE: Given that the temperature of the copper wire is increased by 10°C, from 20°C to 30°C, we can calculate the percentage increase in resistance. Let R0 be the resistance at 20°C and R be the resistance at 30°C. Using the given formula, we can calculate the ratio of R to R0 as (R/R0) = (1 + α(30 - 20)) = (1 + 10α). To find the percentage increase, we can calculate ((R - R0)/R0) × 100%.

⚠️ COMMON MISTAKE: Students often fail to consider the initial temperature (T0) while calculating the percentage increase in resistance, which can lead to incorrect results.