Question

deduce ohm's law from elementary ideas and hence write an expression for resistance and resistivity​

Answer 1

Answer:

Ohm's Law states that: Electric current flowing through a circuit is directly proportional to the potential difference between the two ends of the conductor.

V is directly proportional to I

V = I×R

where R is the constant of proportionality called Resistance for a given conductor, for a given temperature.

Answer 2

Answer:

R=ρlA is right expression for resistance and resistivity​.

Explanation:

Step 1: The fundamental principle of Ohm's law asserts that, under unaltered physical conditions, the potential difference V across a conductor is directly proportional to the current I flowing through it.

i.e. $V \alpha I$

or $\frac{V}{I}=$ constant (R)

Where $\mathrm{R}$ is the constant known ar resistance of the conductor. Resistance is directly proportional to the length of the conductor and inversely proportional to the area of cross section $\mathrm{n}$ of the conductor.

Therefore,

$RolA$,

Where $\mathrm{R}, \mathrm{I}$ and $\mathrm{A}$ are resistance, length and area of cross section respectively.

Step 2: On removing the sign of proportionality,

we get:

$R=\rho l A$,

where

$\rho$ is the resistivity of the conductor of resistance $\mathrm{R}$ which depends on the nature of the conductor.

Now $I=n e A v d_1$

Step 3: Where $\mathrm{n}$ is the number of electrons present in unit volume

of the conductor drifting with velocity vd.

But $v d=e E m \tau_{\text {, }}$

so putting the value of vd in the above eqn of current, we get, $I=n e A \times e E m \tau$ further we know that $\mathrm{E}=\mathrm{VI}$,

so $I=n e A \times e V m l \tau$

Again $V I=R=m \ln e^2 A \tau$

and $\rho=R A l=m n e^{2_\tau}$

These are the required expressions.

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