A wire has a resistance of 5 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?

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Q: A wire has a resistance of 5 Ω at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?

Solution: R = R0(1 + α(T - T0)) = 5(1 + 0.004(100 - 20)) = 6.4 Ω.

Steps: 10

Step 1: Identify the initial resistance (R0) of the wire, which is 5 Ω.
Step 2: Identify the initial temperature (T0), which is 20°C.
Step 3: Identify the final temperature (T), which is 100°C.
Step 4: Identify the temperature coefficient of resistivity (α), which is 0.004/°C.
Step 5: Use the formula for resistance change with temperature: R = R0(1 + α(T - T0)).
Step 6: Calculate the change in temperature (T - T0): 100°C - 20°C = 80°C.
Step 7: Multiply the temperature coefficient (α) by the change in temperature: 0.004 * 80 = 0.32.
Step 8: Add 1 to the result from Step 7: 1 + 0.32 = 1.32.
Step 9: Multiply the initial resistance (R0) by the result from Step 8: 5 Ω * 1.32 = 6.6 Ω.
Step 10: The final resistance at 100°C is 6.6 Ω.