In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that:

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) \(R\left( T \right) = {R_o}{e^{-{T^2}/T_0^2}}\)

Step-by-step Solution

Detailed explanation

\(\frac{\frac{1}{T^{2}}}{\frac{1}{T_{0}^{2}}}+\frac{\ln R(T)}{\ln R\left(T_{0}\right)}=1\)

\(\Rightarrow \ln \mathrm{R}(\mathrm{T})=\ln \mathrm{R}\left(\mathrm{T}_{\mathrm{o}}\right)\left(1-\frac{\mathrm{T}_{\mathrm{o}}^{2}}{\mathrm{T}^{2}}\right)\)

\({\rm{R}}({\rm{T}}) = {{\rm{R}}_0}{{\rm{e}}^{ - \left( {\frac{{T_0^2}}{{{T^2}}}} \right)}}\)

Same subject

A thin rod \(MN\), free to rotate in the vertical plane about the fixed end \(N\), is held horizontal . When the end \(M\) is released the speed of this end, when the rod makes an angle \(\alpha \) with the horizontal, will be proportional to ( see figure)

JEE Mains 2018 Hard
The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )

JEE Mains 2026 Easy
A mixture of hydrogen and oxygen has volume \(2000 \; cm ^{3}\), temperature \(300 \; K\), pressure \(100 \; kPa\) and mass \(0.76 \; g\) The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be

JEE Mains 2022 Medium
in circular plate of mass \(M\) and radius \(R\) has its density varying as \(p\left( r \right) = {p_0}\,r\) with \(P_0\) as constant and \(r\) is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I = aMR^2\) . The value of the coefficient \(a\) is

JEE Mains 2019 Hard
Which of the four resistances \(P, Q, R\) and \(S\) generate the greatest amount of heat when a current flows from \(A\) to \(B\) ?

JEE Mains 2013 Hard
A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))

JEE Mains 2013 Hard

Explore more questions on app

From JEE Mains

In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................

JEE Mains 2022 Medium
The difference of speed of light in the two media \(A\) and \(B\,\left(v_{A}-v_{B}\right)\) is \(2.6 \times 10^{7}\,m / s\). If the refractive index of medium \(B\) is \(1.47\), then the ratio of refractive index of medium \(B\) to medium \(A\) is: (Given : speed of light in vacuum \(\left.c =3 \times 10^{8}\, ms ^{-1}\right)\)

JEE Mains 2022 Hard
The circuit shown here has two batteries of \(8.0\,V\) and \(16.0\,V\) and three resistors \(3\,\Omega ,\,9\,\Omega \) and \(9\,\Omega \) and a capacitor of \(5.0\,\mu F.\) How much is the current \(I\) in the circuit in steady state? ................... \(A\)

JEE Mains 2014 Hard
The distance \(x\) covered by a particle in one dimensional motion varies with time \(t\) as \(\mathrm{x}^{2}=\mathrm{at}^{2}+2 \mathrm{bt}+\mathrm{c.}\) If the acceleration of the particle depends on \(\mathrm{x}\) as \(\mathrm{x}^{-\mathrm{n}},\) where \(\mathrm{n}\) is an integer, the value of \(\mathrm{n}\) is

JEE Mains 2020 Hard
Figure below shows a liquid being pushed out of the tube by a piston having area of cross section \(2.0\,cm ^2\). The area of cross section at the outlet is \(10\,mm ^2\). If the piston is pushed at a speed of \(4\,cm s ^{-1}\), the speed of outgoing fluidis \(.........\,cm s ^{-1}\).

JEE Mains 2023 Easy
Unpolarized light of intensity \(I_0\) incident on surface of a block of glass at Brewster's angle. In that case, which one of ihe following statements is true ?

JEE Mains 2015 Medium

Explore more questions on app