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  1. Problems
  2. /A coil of platinum wire has a resistance of 100.0 Ω at 20 °C…
MediumPhysicsHigh School (11–12)Electricity & Magnetism › Current ElectricityNumericalpython

A coil of platinum wire has a resistance of 100.0 Ω at 20 °C…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A coil of platinum wire has a resistance of 100.0 Ω100.0\ \Omega100.0 Ω at 20 ∘20\ ^\circ20 ∘C. Its temperature coefficient is 3.9×10−33.9 \times 10^{-3}3.9×10−3 per ∘^\circ∘C. The coil is put in a hot bath and reads 128.5 Ω128.5\ \Omega128.5 Ω. What is the temperature of the bath?

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Work it out on paper, then type your number. The answer itself stays hidden.

°C
Need a reminder? The key ideaShowHide

For a metal, RT=R0[1+α(T−T0)]R_T = R_0[1 + \alpha(T - T_0)]RT​=R0​[1+α(T−T0​)], with T0=20 ∘CT_0 = 20\ ^\circ\text{C}T0​=20 ∘C. In a colour code, the first two bands give digits, the third gives the power of ten, and the last gives the tolerance: gold ±5 %\pm 5\ \%±5 %, silver ±10 %\pm 10\ \%±10 %, none ±20 %\pm 20\ \%±20 %.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The formula. R=R0[1+α(T−20)]R = R_0[1 + \alpha(T - 20)]R=R0​[1+α(T−20)]. So RR0−1=α(T−20)\dfrac{R}{R_0} - 1 = \alpha(T - 20)R0​R​−1=α(T−20).

Step 2. The rise. T−20=128.5/100.0−13.9×10−3=0.2853.9×10−3=73.1 ∘CT - 20 = \dfrac{128.5/100.0 - 1}{3.9 \times 10^{-3}} = \dfrac{0.285}{3.9 \times 10^{-3}} = 73.1\ ^\circ\text{C}T−20=3.9×10−3128.5/100.0−1​=3.9×10−30.285​=73.1 ∘C.

Step 3. The temperature. T=20+73.1=93.1 ∘CT = 20 + 73.1 = 93.1\ ^\circ\text{C}T=20+73.1=93.1 ∘C.

Answer: 93.1 ∘93.1\ ^\circ93.1 ∘C.

Check. A rise of 73 ∘73\ ^\circ73 ∘C changes the resistance by 0.0039×73=0.2850.0039 \times 73 = 0.2850.0039×73=0.285, which is 28.5 Ω28.5\ \Omega28.5 Ω on 100 Ω100\ \Omega100 Ω. It fits.

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  1. Temperature and the resistor colour codeCurrent, Drift Velocity and Resistivity

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