Idea of Temperature

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. A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to this current, the temperature of the wire is raised by $\Delta T$ in a time $t$. A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of wire is raised by same amount $\Delta T$ in the same time $t$. Find the value of $N$.

1. $2$
2. $4$
3. $6$
4. $8$

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. 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. $9:1$