Question

A carbon electrode has a resistance of 0.125 ohm at 20 ⁰C the temperature coefficient of carbon is -0.0005 at 20⁰C. what will be the resistance of electrode at 85 ⁰C​

Answer 1

Answer is given in the pic.

Answer 2

Given:

A carbon electrode has a resistance of 0.125 ohm at 20 ⁰C the temperature coefficient of carbon is -0.0005 at 20⁰C.

To find:

Temperature of the electrode at 85°.

Calculation:

Resistance at any temperature w.r.t 0°C will be :

$\boxed{ \sf{R = R_{0}(1 + \alpha \Delta\theta)}}$

At 20° C , we can say:

$\therefore \: \sf{R_{1} = R_{0}(1 + \alpha \Delta\theta)}$

$= > \: \sf{0.125= R_{0} \{1 - ( 5 \times {10}^{ - 4} ) \times(20 - 0) \}}$

$= > \: \sf{0.125= R_{0} \{1 - ( 5 \times {10}^{ - 4} ) \times20 \}}$

$= > \: \sf{0.125= R_{0} \{1 - {10}^{ - 2} \} }$

$= > \: \sf{0.125= R_{0} \{1 - 0.01\} }$

$= > \: \sf{0.125= R_{0} \{0.99\} }$

$= > \: \sf{R_{0} = 0.1262 \: ohm}$

At 85°C , we can say:

$\therefore \: \sf{R_{2} = R_{0}(1 + \alpha \Delta\theta)}$

$= > \: \sf{R_{2} = (0.1262) \{1 -(5 \times {10}^{ - 4} )(85 - 0) \}}$

$= > \: \sf{R_{2} = (0.1262) \{1 -(5 \times {10}^{ - 4} )(85 ) \}}$

$= > \: \sf{R_{2} = (0.1262) \{1 -(425 \times {10}^{ - 4} ) \}}$

$= > \: \sf{R_{2} = (0.1262) \{1 -(0.0425) \}}$

$= > \: \sf{R_{2} = (0.1262) \{0.9575 \}}$

$= > \: \sf{R_{2} = 0.1208 \: ohm}$

So, resistance at 85°C is 0.1208 ohms.