Idea of Temperature

Q. Resistance of a resistor at temperature $t^{\circ }C$ is $R_t=R_0(1+at+b{t}^2)$; where $R_0$ is the resistance at $0^{\circ }C.$ The temperature coefficient of resistance at temperature $t^{\circ }C$ is

1. $\frac{(1+at+b{t}^2)}{a+2bt}$
2. $(a+2bt)$
3. $\frac{a+2bt}{(1+at+b{t}^2)}$
4. $\frac{a+2bt}{2(1+at+b{t}^2)}$

Q. A platinum wire has a resistance of $10\Omega$ at $0^{\circ }C$ and $20\Omega$ at ${273}^{\circ }C$. Find the value of temperature coefficient of platinum.

1. $\frac{1^{\circ }}{273}{C}^{-1}$
2. $\frac{1^{\circ }}{273}{K}^{-1}$
3. $\frac{1^{\circ }}{546}{C}^{-1}$
4. $\frac{1^{\circ }}{546}{K}^{-1}$

Q.

Two resistors with temperature coefficients of resistance ${\alpha }_1$ and ${\alpha }_2$ have resistances $R_1$ and $R_2$ at $0^{\circ }C$. What is the temperature coefficient of the compound resistor consisting of the two resistors connected in parallel?

1. $\frac{R_1{\alpha }_1+{\alpha }_2{R}_2}{R_1+R_2}$

2. $\frac{{\alpha }_1+{\alpha }_2}{2}$

3. $\frac{2{\alpha }_1+{\alpha }_2}{{\alpha }_1+{\alpha }_2}$

4. $\frac{{\alpha }_1{R}_2+{\alpha }_2{R}_1}{R_1+R_2}$

Q. The same mass of copper is drawn into two wires $A$ and $B$ of radii $r$ and $3r$ respectively. They are connected in series, and electric current is passed. The ratio of the heat proiduced in $A$ and $B$ is :

1. $1:9$
2. $1:81$
3. $81:1$
4. $9:1$

Q. The charge flowing through a resistance $R$ varies with time $t$ as $Q=at-b{t}^2$, where $a$ and $b$ are positive constants. The total heat produced in $R$ is:

1. $\frac{a^{3}R}{6b}$
2. $\frac{a^{3}R}{3b}$
3. $\frac{a^{3}R}{2b}$
4. $\frac{a^{3}R}{b}$

Q. Resistance of a resistor at temperature $t^{\circ }C$ is $R_t=R_0(1+at+b{t}^2)$; where $R_0$ is the resistance at $0^{\circ }C.$ The temperature coefficient of resistance at temperature $t^{\circ }C$ is

1. $\frac{(1+at+b{t}^2)}{a+2bt}$
2. $(a+2bt)$
3. $\frac{a+2bt}{(1+at+b{t}^2)}$
4. $\frac{a+2bt}{2(1+at+b{t}^2)}$