B M Sharma Solutions for Chapter: Electric Current and Circuits, Exercise 2: Concept Application Exercise

A coil of wire has a resistance of $25.00 \mathrm{\Omega }$ at $20 °\mathrm{C}$ and resistance of $25.17 \mathrm{\Omega }$ at $35 °\mathrm{C}$. What is its temperature coefficient of resistance?

A metal wire of diameter $2 \mathrm{mm}$ and of length $300 \mathrm{m}$ has a resistance of $1.6424 \mathrm{\Omega }$ at $20 °\mathrm{C}$ and $2.415 \mathrm{\Omega }$ at $150 °\mathrm{C}$. Find the values of $\alpha \text{,} R_0$ and ${\rho }_0,$ where the zero subscripts refers to $0°\mathrm{C},$ and ${\rho }_{20°\mathrm{C}};$ Identify the metal.

It is desired to make a $20 \mathrm{\Omega }$ coil of wire, which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance $R_1$ is placed in series with an iron resistor of resistance $R_2$. The proportions of iron and carbon are so chosen that $R_1+R_2=20 \mathrm{\Omega }$ for all temperatures near $20 °\mathrm{C}$. Find the values of $R_1$ and $R_2$? (${\alpha }_{\text{carbon }}=-0.5\times {10}^{-3 \circ }{\mathrm{C}}^{-1}\text{,} {\alpha }_{\text{iron }}=5\times {10}^{-3 \circ }{\mathrm{C}}^{-1}$).

A resistance thermometer measures temperature with the increase in resistance of a wire of high temperature. If the wire is platinum and has a resistance of $10 \mathrm{\Omega }$ at $20 °\mathrm{C}$ and resistance of $35 \mathrm{\Omega }$ in a hot furnace, what is the temperature of the furnace? $\left({\alpha }_{\text{platinum }}=0.0036 °{\mathrm{C}}^{-1}\right)$

A conductive wire has a resistance of $10 \mathrm{ohm}$ at $0°\mathrm{C}$ and $\alpha$ is $\frac{1}{273} °{\mathrm{C}}^{-1}$, then determine its resistance at $273 °\mathrm{C}$.

What is the drift speed of the conduction electrons in a copper wire with radius $r=900 \mu \mathrm{m}$ when it has a uniform current $i=17 \mathrm{mA}$? Assume that each copper atom contributes one conduction electron to the current and the current density is uniform across the wire's cross-section. (The density of copper is $\rho =9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and atomic mass of copper is $M=63.5 \mathrm{amu}$)

(a) At what temperature would the resistance of a copper conductor be double its value of $0°\mathrm{C}?$

(b) Does this same temperature hold for all copper conductors, regardless of shape and size? $\left[{\alpha }_{\mathrm{C}}=4.0\times {10}^{-3}{ °\mathrm{C}}^{-1}\right]$

A potential difference is applied across the filament of a bulb at $t=0,$ and it is maintained at a constant value while the filament gets heated to its equilibrium temperature. We find that the final current in the filament is one-sixth of the current drawn at $t=0.$ If the temperature of the filament at $t=0$ is $20 °\mathrm{C}$ and the temperature coefficient of resistivity at $20 °\mathrm{C}$ is $0.0043 {{}^{\circ }\mathrm{C}}^{-1},$ find the final temperature of the filament.