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A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of re

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Question: A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?

Options:

  1. 10.4 ohms
  2. 12 ohms
  3. 14 ohms
  4. 16 ohms

Correct Answer: 12 ohms

Solution: 

R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10.4 ohms.

A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of re

Practice Questions

Q1
A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
  1. 10.4 ohms
  2. 12 ohms
  3. 14 ohms
  4. 16 ohms

Questions & Step-by-Step Solutions

A wire has a resistance of 10 ohms at 20°C. If the temperature coefficient of resistivity is 0.004/°C, what will be its resistance at 100°C?
  • Step 1: Identify the initial resistance (R0) of the wire, which is 10 ohms.
  • 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: Calculate the change in temperature (T - T0), which is 100°C - 20°C = 80°C.
  • Step 6: Multiply the change in temperature by the temperature coefficient: 0.004 * 80 = 0.32.
  • Step 7: Add 1 to the result from Step 6: 1 + 0.32 = 1.32.
  • Step 8: Multiply the initial resistance (R0) by the result from Step 7: 10 ohms * 1.32 = 13.2 ohms.
  • Step 9: The final resistance at 100°C is 13.2 ohms.
  • Resistance and Temperature Relationship – The resistance of a conductor changes with temperature, and this relationship is quantified by the temperature coefficient of resistivity.
  • Temperature Coefficient of Resistivity – This coefficient indicates how much the resistance of a material changes per degree Celsius change in temperature.
  • Linear Approximation of Resistance Change – The formula R = R0(1 + α(T - T0)) is used to calculate the new resistance based on initial resistance, temperature change, and temperature coefficient.
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