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Current Electricity MCQs for NEET — Physics Questions with Answers

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A wire of radius r has resistance R. If it is stretched to a radius of $\frac{3 r}{4}$ , its resistance becomes

$\frac{9 R}{16}$

$\frac{16 R}{9}$

$\frac{81 R}{256}$

$\frac{256 R}{81}$

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Explanation

$R = ρ \frac{l}{A} W h e n t h e w i r e i s s t r e t c h e d t o a n e w l e n g t h, i t s v o l u m e r e m a i n s c o n s \tan t . \Rightarrow A_{1} l_{1} = A_{2} l_{2} \Rightarrow \frac{l_{1}}{l_{2}} = \frac{A_{2}}{A_{1}} \frac{R_{1}}{R_{2}} = \frac{l_{1}}{A_{1}} \times \frac{A_{2}}{l_{2}} = {(\frac{A_{2}}{A_{1}})}^{2} \Rightarrow \frac{R_{1}}{R_{2}} = {(\frac{r_{2}}{r_{1}})}^{4}$

⇒ $\frac{R}{R_{2}} = {(\frac{3 r / 4}{r})}^{4} = \frac{81}{256} = R_{2} = \frac{256}{81} R$

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A copper wire has a square cross-section, 2.0 mm on a side. It carries a current of 8 A and the density of free electrons is 8 × 10²⁸ m^–3. The drift speed of electrons is equal to

0.156 × 10^–3 m.s^–1

0.156 × 10^–2 m.s^–1

3.12 × 10^–3 m.s^–1

3.12 × 10^–2 m.s^–1

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Explanation

$v_{d} = \frac{i}{n A e} = \frac{8}{8 \times 10^{28} \times {(2 \times 10^{- 3})}^{2} \times 1 .6 \times 10^{- 19}}$

= $0 .156 \times 10^{- 3} m / s e c$ .

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What length of the wire of specific resistance $48 \times 10^{- 8} Ω m$ is needed to make the resistance of 4.2 Ω (diameter of wire = 0.4 mm)

4.1 m

3.1 m

2.1 m

1.1 m

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Explanation

$l = \frac{R π r^{2}}{ρ}$

$= \frac{4 .2 \times 3 .14 \times {(0 .2 \times 10^{- 3})}^{2}}{48 \times 10^{- 8}} = 1 .1 m$

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A strip of copper and another of germanium are cooled from room temperature to 80 K. The resistance of

Each of these increases

Each of these decreases

Copper strip increases and that of germanium decreases

Copper strip decreases and that of germanium increases

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Explanation

For conductors, resistance ∝ Temperature and for semi-conductor, resistance ∝ $\frac{1}{Temperature}$

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In a hydrogen discharge tube, it is observed that through a given cross-section 3.13 × 10¹⁵ electrons are moving from right to left and 3.12 × 10¹⁵ protons are moving from left to right. What is the electric current in the discharge tube and what is its direction :

1 mA towards the right

1 mA towards left

2 mA towards left

2 mA towards the right

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A resistance R is stretched to four times its length. Its new resistance will be

4 R

64 R

R/4

16 R

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Explanation

$R' = n^{2} R \Rightarrow R' = 16 R$

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What is the resistance of a carbon resistance which has bands of colours brown, black and brown

100 Ω

1000 Ω

10 Ω

1 Ω

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Explanation

Significant figures		Multiplier
Brown	Black	Brown
1	0	10¹

∴ R = 10 × 10¹ = 100 Ω

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The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then :

The resistance will be doubled and the specific resistance will be halved

The resistance will be halved and the specific resistance will remain unchanged

The resistance will be halved and the specific resistance will be doubled

The resistance and the specific resistance, will both remain unchanged

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Explanation

$R \propto \frac{l}{r^{2}}$ ⇒ $\frac{R_{2}}{R_{1}} = \frac{l_{2}}{l_{1}} \times \frac{{r_{1}}^{2}}{{r_{2}}^{2}}$ = $(\frac{2}{1}) \times {(\frac{1}{2})}^{2}$ $= \frac{1}{2}$

⇒ $R_{2} = \frac{R_{1}}{2},$ specific resistance doesn't depend upon length, and radius.

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The following four wires are made of the same material and are at the same temperature. Which one of them has highest electrical resistance :

Length = 50 cm, diameter = 0.5 mm

Length = 100 cm, diameter = 1 mm

Length = 200 cm, diameter = 2 mm

Length = 300 cm, diameter = 3 mm

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Explanation

$R \propto \frac{l}{r^{2}}$ .

For highest resistance $\frac{l}{r^{2}}$ should be maximum, which is correct for option

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The colour sequence in a carbon resistor is red, brown, orange and silver. The resistance of the resistor is

21 × 10³ ± 10%

23 × 10¹ ± 10

21 × 10³ ± 5%

12 × 10³ ± 5%

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Explanation

Significant figures		Multiplier	Tolerance
Red	Brown	Orange	Silver
2	1	10³	± 10%

∴ R = $21 \times 10^{3} \pm 10 %$

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