Answer

Verified

381.9k+ views

**Hint:**The temperature coefficient of a material is the relative change of its physical properties with the change in temperature. If the material of the two resistances will not change then the initial sum of temperature coefficients should equal the final sum after time t.

**Complete answer:**

According to the question, let us consider two resistances ${{R}_{1}}$ and ${{R}_{2}}$ made of different materials. Their temperature coefficients are, $\alpha $and $-\beta $ respectively.

Resistance and temperature coefficient relation is given by the following equation,

$R={{R}_{0}}(1+\alpha \Delta t)$

Where, ${{R}_{0}}$ is initial or reference temperature at temperature ${{T}_{0}}$ and $\Delta t$is $T-{{T}_{0}}$.

In this case, the resistance will not change so, using the above formula, we can write,

$\begin{align}

& {{R}_{1}}+{{R}_{2}}={{R}_{1}}(1+\alpha T)+{{R}_{2}}(1-\beta T) \\

& \Rightarrow {{R}_{1}}\alpha T={{R}_{2}}\beta T \\

& \Rightarrow \dfrac{{{R}_{1}}}{{{R}_{2}}}=\dfrac{\beta }{\alpha } \\

\end{align}$

Thus, the material of ${{R}_{1}}$ and ${{R}_{2}}$will not change with temperature if $\dfrac{{{R}_{1}}}{{{R}_{2}}}$ equal to $\dfrac{\beta }{\alpha }$.

**Hence, the correct answer is option (D).**

**Additional Information:**

Temperature coefficients of materials have useful applications in electric and magnetic properties of material. Normally, the value of temperature coefficient lies between $-2$ and $3$.

The resistance and temperature coefficient relation ($R={{R}_{0}}(1+\alpha \Delta t)$) is a linear approximation, if temperature coefficient of material does not vary too much with temperature, i.e. $\alpha \Delta t\langle \langle 1$

The temperature coefficient of elasticity i.e. the elastic modulus of elastic materials decreases with the increase in temperature.

Temperature coefficient has a dimension that is reverse of temperature. Unit of temperature coefficient is $\kappa^{-1}$(per Kelvin). Sometimes thermal coefficient is expressed as ppm/$^{0}C$ or ppm/K, ppm is parts per million.

**Note:**

The resistance and temperature coefficient relation ($R={{R}_{0}}(1+\alpha \Delta t)$) is important to remember for solving similar question, however this relation is a linear approximation and is only applicable for small temperature differences ($\Delta t$) between initial and final temperature changes.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How many crores make 10 million class 7 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths