To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at $25^{\circ} \mathrm{C}$ and resistance of the semiconductor arm is $3 \mathrm{~m} \Omega$. Arm BC is cooled at a constant rate of $2^{\circ} \mathrm{C} / \mathrm{s}$. If the galvanometer $\mathrm{G}$ shows no deflection after $10 \mathrm{~s}$, then $\alpha$ is :
JEE MAIN 2024, Diffcult
Download our app for free and get started
For no deflection $\frac{0.8}{1}=\frac{R}{3}$
$\Rightarrow \mathrm{R}=2.4 \mathrm{~m} \Omega$
Temperature fall in $10 \mathrm{~s}=20^{\circ} \mathrm{C}$
$\Delta \mathrm{R}=\mathrm{R} \alpha \Delta \mathrm{t}$
$\alpha=\frac{\Delta \mathrm{R}}{\mathrm{R} \Delta \mathrm{t}}=\frac{-0.6}{3 \times 20}$
$=-10^{-2} \mathrm{C}^{-1}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The equivalent resistance of the circuit shown below between points $a$ and $b$ is $..........\Omega$View Solution
- 2There are $n$ similar conductors each of resistance $R$. The resultant resistance comes out to be $x$ when connected in parallel. If they are connected in series, the resistance comes out to beView Solution
- 3A uniform wire of resistance $9$ $\Omega$ is cut into $3$ equal parts. They are connected in the form of equilateral triangle $ABC$. A cell of $e.m.f.$ $2\,V$ and negligible internal resistance is connected across $B$ and $C$. Potential difference across $AB$ is ............... $V$View Solution
- 4The internal resistances of two cells shown are $0.1\,\Omega $ and $0.3\,\Omega $. If $R = 0.2\,\Omega $, the potential difference across the cellView Solution
- 5Effective resistance between $A$ and $B$ is ........... $\Omega$View Solution
- 6In the figure shown, what is the current (in Ampere) drawn from the battery ? You are given $R_1 = 15\,\Omega $$,R _2 = 10\,\Omega ,$$ R_3 = 20\,\Omega ,$$ R_4 = 5\,\Omega ,$$R_5 = 25\,\Omega ,$$R_6 = 30\,\Omega , $$E = 15\,V$View Solution
- 7In a large building, there are $15$ bulbs of $40\ W$, $5$ bulbs of $100\ W, 5$ fans of $80\ W$ and $1$ heater of $1\ kW$. The voltage of electric mains is $220\ V$. The minimum capacity of the main fuse of the building will be ................ $A$View Solution
- 8Two sources of equal $emf$ are connected to an external resistance $R$. The internal resistances of the two sources are ${R_1}$ and ${R_2}\,({R_2} > {R_1})$. If the potential difference across the source having internal resistance ${R_2}$ is zero, thenView Solution
- 9The value of current through $20\,\Omega $ resistor is .................. $A$View Solution
- 10Consider a metallic cube of edge length $L$. Its resistance, $R$, measured across its opposite faces is $R =\frac{ m _{ e } v }{ ne ^2 L ^2}$, where $n$ is the number density and $v$ is the drift speed of electrons in the cube, and $e$ and $m _{ e }$ are the charge and mass of an electron respectively. Assuming the de-Broglie wavelength of the electron to be $L$, the maximum resistance of the sample is closest to ............. $\,\Omega$ $\left(e=1.60 \times 10^{-19} \,C ; m _{ e }=9.11 \times 10^{-31} \,kg\right.$; Planck's constant, $h=6.63 \times 10^{-34} \,Js$ )View Solution