Problem

A carbon electrode has a resistance of $0.125 \, \Omega$ at $20^\circ \mathrm{C}$. The temperature coefficient of resistance for carbon is $-0.0005$. What will be the resistance of the electrode at $85^\circ \mathrm{C}$?

Data

• Initial resistance: $R_0 = 0.125 \, \Omega$
• Initial temperature: $T_1 = 20^\circ \mathrm{C}$
• Final temperature: $T_2 = 85^\circ \mathrm{C}$
• Temperature coefficient: $\alpha = -0.0005$

Prerequisite Concept

• Temperature-Dependent Resistance:
  $R_T = R_0 (1 + \alpha \Delta T), \, \Delta T = T_2 - T_1$

Solution

1. Temperature change:
   $\Delta T = T_2 - T_1 = 85 - 20 = 65^\circ \mathrm{C}$

2. Resistance at $T_2$:
   $R_T = 0.125 (1 + (-0.0005)(65))$
   $R_T = 0.125 (1 - 0.0325) = 0.125 \cdot 0.9675 = 0.12 \, \Omega$

Answer

• Resistance at $85^\circ \mathrm{C}$: $R_T = 0.12 \, \Omega$

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