The V-I graph for a conductor at temperatures | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The $V-I$ graph for a conductor at temperatures $T_1$ and $T_2$ is shown in the figure.We know that the resistance $R$ of a conductor is directly

Vedclass · Accepted Answer

$\cot 2 	heta$

Vedclass · Answer

(C) The $V-I$ graph for a conductor at temperatures $T_1$ and $T_2$ is shown in the figure.We know that the resistance $R$ of a conductor is directly proportional to its temperature $T$ (i.e.,$R \propto T$).For the $V-I$ graph,the slope represents the resistance $R = \frac{V}{I}$.From the figure,the slope of the line for $T_1$ with respect to the $I$-axis is $	an 	heta$. Thus,$R_1 \propto 	an 	heta \Rightarrow R_1 = K 	an 	heta$,where $K$ is a constant.Similarly,the slope of the line for $T_2$ with respect to the $I$-axis is $	an(90^{\circ}-	heta) = \cot 	heta$. Thus,$R_2 \propto \cot 	heta \Rightarrow R_2 = K \cot 	heta$.Therefore,$T_2 - T_1 \propto R_2 - R_1 = K(\cot 	heta - 	an 	heta)$.$T_2 - T_1 \propto K \left( \frac{\cos 	heta}{\sin 	heta} - \frac{\sin 	heta}{\cos 	heta} ight) = K \left( \frac{\cos^2 	heta - \sin^2 	heta}{\sin 	heta \cos 	heta} ight)$.Using trigonometric identities $\cos^2 	heta - \sin^2 	heta = \cos 2 	heta$ and $\sin 	heta \cos 	heta = \frac{1}{2} \sin 2 	heta$,we get:$T_2 - T_1 \propto K \left( \frac{\cos 2 	heta}{\frac{1}{2} \sin 2 	heta} ight) = 2K \cot 2 	heta$.Thus,$T_2 - T_1 \propto \cot 2 	heta$.

The $V-I$ graph for a conductor at temperatures $T_1$ and $T_2$ is as shown in the figure. $T_2-T_1$ is proportional to

Similar Questions

Write the limitations of Ohm's law.

All of the following statements are true except:

Explain the statement: "$V \to I$ relation is not always a one-one function."

Ohm's law is true for which of the following?

Of the following graphs,the one that correctly represents the $I-V$ characteristics of an 'Ohmic device' is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module