Bob, please confirm if I got this right and if not, please help to solve
1)A wire has a resistance of 10 ohm at 20 deg celsius and 13.1 ohm at 100 deg celsius. Obtain a value for its temperature coefficient of resistance.
ans I got is this=
using Rt = Ro (1 + alpha(T-To))
13.1=10(1 + alpha(100-20))
13.1 = 10(1+80 alpha)
alpha = 3.1/800 = 0.003875
I didn't do the calc, but you did the right algebra.
... and don't foget the units.
Yes, you have correctly set up the equation using the formula for resistance with temperature coefficient. To solve the equation, you'll need to rearrange it to isolate the variable alpha, which represents the temperature coefficient of resistance.
The equation you started with is:
13.1 = 10(1 + alpha(100 - 20))
To solve for alpha, follow these steps:
1. Start by distributing the 10 on the right side of the equation:
13.1 = 10 + 10alpha(100 - 20)
2. Simplify the equation:
13.1 = 10 + 1000alpha - 200alpha
3. Combine like terms:
13.1 = 10 + 800alpha
4. Subtract 10 from both sides to isolate the term with alpha:
13.1 - 10 = 800alpha
5. Simplify:
3.1 = 800alpha
6. Divide both sides by 800:
alpha = 3.1 / 800
Now, let's evaluate the division:
alpha ≈ 0.003875
You got the correct value for alpha. Just remember to include the units for the temperature coefficient of resistance, which is typically expressed in per degree Celsius (°C⁻¹). Now you can confirm your result, alpha = 0.003875 °C⁻¹.