Question

the resistance of a conductor is 10 ohm at 50 degree celcius and 15 ohm at 100 degree celcius .calculate its resistance at 0 degree celcius. numerical problem

Answer 1

Answer:

See below

Explanation:

Take Rt=R0[1+(alpha)t]

Where R0 is the resistances at 273 K

Form equations at both temperature by the above general formula

Find R0

Done.

Answer 2

Answer:

The resistance of a conductor is 10 ohm at 50° and 15 ohm at 100°. What is the resistance at 0°?

We start by noting down the law that will be used:

R=Rref[1+α(T−Tref)]

Where:

R - Conductor resistance at temperature T .

Rref - Conductor resistance at reference temperature Tref , usually 20∘C , but sometimes 0∘C .

α - Temperature coefficient of resistance for conductor material.

T - Conductor temperature in degrees Celcius.

Tref - Reference temperature that α is specified at for the conductor material.

Second let’s try detecting the temperature coefficient α , because we have 2 cases and also we do not know the material.

First case:

R=15 Ω

T=100∘C

Rref=10 Ω

Tref=50∘C

Be noted that α will be at Tref=50∘C , substituting:

15=10[1+α(100−50)]

1510=1+50α

0.5=50α

Then:

α=0.01 per degree Celsius

Now let’s calculate the resistance at 0∘C :

R=?

T=0∘C

Rref=10 Ω

Tref=50∘C

α=0.01 per degree Celsius ( @Tref )

R=10[1+0.01∗(0−50)]=10∗0.5=5 Ω - This is the answer.

You noted that at 0∘C temperature it was 5 Ω , then by increasing to 50∘C it's 10 Ω and by increasing to 100∘C it's 15 Ω . By increasing temperature the resistance increases.

Explanation:

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