The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law-R-R0-1-T-T0-The resistance is 101-6 - at the triple-point of water 273-16 K- and 165-5 - at the normal melting point of lead 600-5 K - What is the temperature when the resistance is 123-4 - -

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Resistance Thermometers

The electrica...

Question

The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:

R = R_o [1 + α (T – T_o)]

The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?

Open in App

Solution

It is given that:

R = R₀ [1 + α (T – T₀)] … (i)

Where,

R₀ and T₀ are the initial resistance and temperature respectively

R and T are the final resistance and temperature respectively

α is a constant

At the triple point of water, T₀ = 273.15 K

Resistance of lead, R₀ = 101.6 Ω

At normal melting point of lead, T = 600.5 K

Resistance of lead, R = 165.5 Ω

Substituting these values in equation (i), we get:

For resistance, R₁ = 123.4 Ω

Suggest Corrections

Similar questions

Q. The electrical resistance of pure platinum increases linearly with increasing temperature over a small range of temperature. This property is used in a Platinum resistance thermometer. The relation between

R_{θ}

(Resistance at

θ K

) and

R_{0}

(Resistance at

θ_{0} K)

is given by

R_{θ} = R_{0} [1 + α (θ - θ_{0})]

, where

α =

temperature coefficient of resistance. Now, if a Platinum resistance thermometer reads

0^{\circ} C

when its resistance is

80 Ω

and

100^{\circ} C

when its resistance is

90 Ω

, find the temperature at which its resistance is

86 Ω

Q. The temperature coefficient of resistance of a conductor varies as

α (T) = 3 T^{2} + 2 T

. If

R_{0}

is resistance at

T = 0

and

R

is resistance at

T

, then

Q. The temperature coefficient of resistance of conductor varies as

α (T) = 3 T^{2} + 2 T

. If

R_{0}

is resistance at

T = 0

and

R

is resistance at

T

, then

Q. The resistance of an electrical toaster has a temperature dependence given by

R (T) = R_{0} [1 + α (T - T_{0})]

in its range of operation. At

T_{0} = 300 K, R_{0} = 100 Ω

and at

T = 500 K, R = 120 Ω

. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is :

A resistance thermometer reads R = 20.0 $Ω$ , 27.5 $Ω$ , and 50.0 $Ω$ at the ice point ( $0^{\circ} C$ ), the steam point ( $100^{\circ} C$ ) and the zinc point ( $420^{\circ} C$ ) respectively. Assuming that the resistance varies with temperature as $R_{θ} = R_{0} (1 + α θ + β θ^{2})$ , find the values of $R_{0}, α$ and $β$ . Here $θ$ represents the temperature on Celsius scale.

Join BYJU'S Learning Program