Question

Consider a conductor of resistance r, length l thickness d and resistivity p.now this conductor is cut into four equal parts. what will be the new resistivity of each of these parts.why? find the resistance if all of these parts are connected in series and parallel​

Answer 1

New Resistivity

According to the question, the conductor is divided into four equal parts. Also, there is no change in length or thickness of the conductor.

Now, we know that resistivity depends on the nature as well as the size of a conductor. Then, in the given case, the resistivity remains the unchanged.

Pattern of Conductor Connection

Consider the total length to be $L$

So, the length of each part = $\frac{L}{4}$

Likewise, the resistance of each part = (ρL/4)/A

Then, the resistance of the each part = $\frac{R}{4}$ = $R_1$ = $R_2$ = $R_3$ = $R_4$

(i) Parallel form

$\frac{1}{Reqv}$ = $\frac{1}{R_1}$ + $\frac{1}{R_2}$ + $\frac{1}{R_3}$ + $\frac{1}{R_4}$

⇒ $\frac{1}{Reqv}$ = $\frac{4}{R}$ +  $\frac{4}{R}$ +  $\frac{4}{R}$ +  $\frac{4}{R}$

∴ $\frac{1}{Reqv}$ = $\frac{16}{R}$

∴ $Reqv$ = $\frac{R}{16}$ Ω

(ii) Series form

$Reqv$ = $R_1$ + $R_2$ + $R_3$ + $R_4$

⇒ $Reqv$ = $\frac{R}{4}$ +  $\frac{R}{4}$ +  $\frac{R}{4}$ +  $\frac{R}{4}$

∴ $Reqv$ = $R$ Ω

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