Question: Q. 3. A metal rod of length $10 \mathrm{~cm}$ and a rectangular cross-section of $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ is connected to a battery across opposite faces. The resistance will be
(a) maximum when the battery is connected across $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ faces.
(b) maximum when the battery is connected acyoss $10 \mathrm{~cm} \times 1 \mathrm{~cm}$ faces.
(c) maximum when the battery is connected across $10 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ faces.
ใf Very Shorf Answer Type Questions
(1 mark each)
Q. 1. Define the conductivity of a conductor. Write its SI unit. R [O.D. Compt I, II, III 2017]
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Solution:
Ans. Definition
SI Unit
Conductivity is reciprocal of resistivity
$$ \sigma=\frac{1}{\rho} $$
SI unit : $\mathrm{S}$ (siemen)
[CBSE Marking Scheme, 2017]
Detailed Answer :
Conductivity of a conductor is the reciprocal of its resistivity i.e.,
$$ \sigma=\frac{1}{\rho}=\frac{n e^{2} \tau}{m} $$
SI unit of conductivity is siemens per metre and is represented as $(\mathrm{S} / \mathrm{m})$. (d) same irrespective of the three faces.
[NCERT Exemplar]
Ans. Correct option : (a)
Explanation: As we know that,
$$ R=\rho\left(\frac{l}{A}\right) $$
The maximum resistance will be achieved when the value of $\frac{l}{A}$, is maximum, so that ’ $A$ ’ must be minimum and it is minimum when area of cross section is $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$.
