Electric Resistance and Simple Circuits | Physics JEE previous year questions with Solutions

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Topic Question Set

Q 11 :

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $n \times 10^{- 3} Ω$ . If the resistivity of the material is $2.4 \times 10^{- 8} Ω m$ , the value of $n$ is ________. [2023]

0%

(2)

$R = ρ \frac{l}{A}, the cross-sectional area is π (b^{2} - a^{2})$

$R = ρ \frac{l}{π (b^{2} - a^{2})} = \frac{2.4 \times 10^{- 8} \times 3.14}{3.14 \times (4^{2} - 2^{2}) \times 10^{- 6}} = 2 \times 10^{- 3} Ω$

$\Rightarrow n = 2$

Q 12 :

If a copper wire is stretched to increase its length by 20%, the percentage increase in resistance of the wire is ______ %. [2023]

0%

(44)

$As volume is constant.$

$So resistance \propto {(length)}^{2}$

$\Rightarrow % change in resistance = 20 + 20 + \frac{400}{100} = 44 %$

Q 13 :

A current of 2 A flows through a wire of cross-sectional area $25.0 {mm}^{2}$ . The number of free electrons in a cubic meter are $2.0 \times 10^{28}$ . The drift velocity of the electrons is ____ $\times 10^{- 6} {ms}^{- 1}$ (given, charge on electron $= 1.6 \times 10^{- 19} C$ ). [2023]

0%

(25)

$Drift velocity$

$v_{d} = \frac{I}{n e A} = \frac{2}{2 \times 10^{28} \times 1.6 \times 10^{- 19} \times 25 \times 10^{- 6}}$

$= 25 \times 10^{- 6} {ms}^{- 1}$

Q 14 :

The number density of free electrons in copper is nearly $8 \times 10^{28} m^{- 3}$ . A copper wire has its area of cross section $= 2 \times 10^{- 6} m^{2}$ and is carrying a current of 3.2 A. The drift speed of the electrons is _______ $\times 10^{- 6} {ms}^{- 1}$ . [2023]

0%

(125)

$n = 8 \times 10^{28} m^{- 3}, Area = 2 \times 10^{- 6} m^{2}, I = 3.2 A$

$I = n e A v_{d}$

$v_{d} = \frac{I}{n e A} = 125 \times 10^{- 6} m/s$

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