CBSE Class 10 Science 2023: question 36(a)

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1. (i) Resistance: Resistance is the property of a conductor by which it opposes the flow of charge (electric current) through it. By Ohm's law, $R=\frac{V}{I}$.

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2. **SI unit – ohm ($\Omega$):** A conductor has a resistance of $1\Omega$ if a current of $1$ A flows through it when a potential difference of $1$ V is applied across its ends, i.e. $1\Omega =\frac{1\text{ V}}{1\text{ A}}$.

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3. (ii) Resistance of a conductor depends on (any two): (1) its length $l$ ($R\propto l$); (2) its area of cross-section $A$ ($R\propto \frac{1}{A}$); (3) the nature of its material; (4) its temperature.

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4. (iii) For a wire of radius $r$: $R=\rho \frac{l}{A}=\rho \frac{l}{\pi r^2}$.

   (1) If only the length is doubled ($l\to 2l$), $R_1=\rho \frac{2l}{\pi r^2}=2R$, so the resistance doubles because $R\propto l$.

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5. (2) If the radius is also doubled ($l\to 2l$, $r\to 2r$):
   $R^{\prime }=\rho \frac{2l}{\pi (2r{)}^2}=\rho \frac{2l}{4\pi r^2}=\frac{1}{2}\rho \frac{l}{\pi r^2}=\frac{R}{2}$.

   The resistance becomes half of its original value. Doubling the radius makes the area of cross-section four times larger, which outweighs the doubling of length.

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Answer: (i) Opposition to the flow of current, $R=V/I$; $1\Omega$ = 1 V/1 A. (ii) Length and area of cross-section (also material, temperature). (iii) Length doubled alone gives $2R$; length and radius both doubled gives $R^{\prime }=R/2$.

Revise the chapter

• Chapter: Electricity (notes, formulas, where marks are lost and every past question)