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

Q 1 :

The electric current through a wire varies with time as $I = I_{0} + β t$ where $I_{0} = 20 A$ and $β = 3 A / s .$ The amount of electric charge crossed through a section of the wire in 20 sec is [2024]

80 C
1000 C
800 C
1600 C

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(2)

Given that, current $I = I_{0} + β t$

Also, $I_{0} = 20 A$ and $β = 3 A / s$

Hence, $d q / d t = 20 + 3 t \Rightarrow d q = (20 + 3 t) d t$

$\int_{0}^{q} d q = \int_{0}^{20} (20 + 3 t) d t$

$\Rightarrow q = {[20 t + \frac{3 t^{2}}{2}]}_{0}^{20} = 1000 C$

Q 2 :

The current in a conductor is expressed as $I = 3 t^{2} + 4 t^{3}$ , where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1 s$ to $t = 2 s$ is _________ C. [2024]

(22) $I = 3 t^{2} + 4 t^{3}$

$\int d Q = \int I d t$

$Q = \int_{1}^{2} (3 t^{2} + 4 t^{3}) d t$

$= {[t^{3} + t^{4}]}_{1}^{2}$

$= (8 + 16) - (2) = 22 C$

Q 3 :

Which of the following resistivity ( $ρ$ ) v/s temperature (T) curve is most suitable to be used in wire bound standard resistors? [2025]

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(1)

For bound standard resistors the resistivity is independent of temperature and remain nearly constant.

Q 4 :

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have [2025]

low thermal conductivity and low electrical conductivity
high thermal conductivity and high electrical conductivity
low thermal conductivity and high electrical conductivity
high thermal conductivity and low electrical conductivity

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(3)

Material should have low thermal conductivity and high electrical conductivity.

Q 5 :

Current passing through a wire as function of time is given as $I$ (t) = 0.02 t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is: [2025]

0.06 C
0.02 C
0.07 C
0.04 C

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(4)

$q = \int i d t = \int_{1}^{2} (0.02 t + 0.01) d t$

$q = {[0.02 \frac{t^{2}}{2} + 0.01 t]}_{1}^{2}$

$= \frac{0.02}{2} \times (2^{2} - 1^{2}) + 0.01 \times 1 = 0.04 C$

Q 6 :

A uniform metallic wire carries a current of 2 A, when a 3.4 V battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{- 3} kg$ , density is $8.92 \times 10^{3} {kg/m}^{3}$ and resistivity is $1.7 \times 10^{- 8} Ω -m$ . The length of the wire is [2023]

$l = 10 m$
$l = 100 m$
$l = 5 m$
$l = 6.8 m$

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(1)

$mass = 8.92 \times 10^{- 3} kg$

$Density, d = 8.92 \times 10^{3} {kg/m}^{3}$

$ρ = 1.7 \times 10^{- 8} Ω - m$

$R = \frac{V}{i} = \frac{3.4}{2} = 1.7 Ω$

$R = \frac{ρ l}{A} = \frac{ρ l^{2}}{vol} = \frac{ρ l^{2} d}{mass} (∵ d = \frac{mass}{vol})$

$l = \sqrt{\frac{R m}{ρ d}} = \sqrt{\frac{1.7 \times 8.92 \times 10^{- 3}}{1.7 \times 10^{- 8} \times 8.92 \times 10^{3}}} = 10 m$

Q 7 :

The resistance of a wire is $5 Ω$ . Its new resistance in ohm, if stretched to 5 times of its original length, will be [2023]

125
5
25
625

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(1)

$∴$ $Volume of wire is constant in stretching$

$V_{i} = V_{f}$

$A_{i} l_{i} = A_{f} l_{f}$

$A l = A' (5 l)$

$A' = \frac{A}{5}$

$R_{f} = \frac{ρ l_{f}}{A_{f}} = \frac{ρ (5 l)}{(\frac{A}{5})} = 25 (\frac{ρ l}{A}) = 25 \times 5 = 125 Ω$

Q 8 :

The charge flowing in a conductor changes with time as $Q (t) = α t - β t^{2} + γ t^{3},$ where $α$ , $β$ and $γ$ are constants. Minimum value of current is [2023]

$α - \frac{3 β^{2}}{γ}$
$α - \frac{γ^{2}}{3 β}$
$β - \frac{α^{2}}{3 γ}$
$α - \frac{β^{2}}{3 γ}$

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(4)

$Q = (α t - β t^{2} + γ t^{3})$

$i = \frac{d Q}{d t} = (α - 2 β t + 3 γ t^{2})$

$\frac{d i}{d t} = (3 γ t - 2 β) = 0 \Rightarrow t = \frac{β}{3 γ}$

$i = (α - 2 β t + 3 γ t^{2}) = (α - \frac{β^{2}}{3 γ})$

Q 9 :

The drift velocity of electrons for a conductor connected in an electrical circuit is $V_{d}$ . The conductor is now replaced by another conductor with the same material and the same length but double the area of cross-section. The applied voltage remains the same. The new drift velocity of electrons will be [2023]

$V_{d}$
$\frac{V_{d}}{2}$
$\frac{V_{d}}{4}$
$2 V_{d}$

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(1)

$i = n A V_{d} e$

$i_{1} = (\frac{V}{R}) and i_{2} = (\frac{2 V}{R})$

$So, \frac{i_{1}}{i_{2}} = \frac{1}{2} = \frac{{(A V_{d})}_{1}}{{(A V_{d})}_{2}} = \frac{V_{d}}{{(V_{d})}_{2}} \times (\frac{1}{2})$

$\frac{1}{2} \times \frac{V_{d}}{{(V_{d})}_{2}} = \frac{1}{2} \Rightarrow {(V_{d})}_{2} = V_{d}$

Q 10 :

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor [2023]

drift from higher potential to lower potential.
move in the curved paths from lower potential to higher potential.
move with the uniform velocity throughout from lower potential to higher potential.
move in the straight line paths in the same direction.

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(2)

$Move in curved path$

$I = n e A V_{d}$

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]

(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]

(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]

(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]

(125)

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

$I = n e A v_{d}$

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

Q 15 :

A cylindrical conductor of length 2 m and area of cross-section $0.2 {mm}^{2}$ carries an electric current of $1.6 A$ when its ends are connected to a $2 V$ battery. Mobility of electrons in the conductor is $α \times 10^{- 3} m^{2} / V . s .$ The value of $α$ is :

$(electron concentration = 5 \times 10^{28} / m^{3} and electron charge = 1.6 \times 10^{- 19} C)$ [2026]

(1)

$V_{d} = μ E = μ \frac{V}{ℓ}$

$I = n e A V_{d}$

$V_{d} = \frac{I}{n e A}$

$μ = \frac{I l}{N n e A}$

$μ = \frac{1.6 \times 3}{2 \times 5 \times 10^{26} \times 1.6 \times 10^{- 19} \times 2 \times 10^{- 7}}$

$μ = 1 \times 10^{- 3} m^{2} / V s$

$α = 1$

Topic Question Set

Q 1 :

The electric current through a wire varies with time as $I = I_{0} + β t$ where $I_{0} = 20 A$ and $β = 3 A / s .$ The amount of electric charge crossed through a section of the wire in 20 sec is [2024]

Q 2 :

The current in a conductor is expressed as $I = 3 t^{2} + 4 t^{3}$ , where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1 s$ to $t = 2 s$ is _________ C. [2024]

Q 3 :

Which of the following resistivity ( $ρ$ ) v/s temperature (T) curve is most suitable to be used in wire bound standard resistors? [2025]

Q 4 :

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have [2025]

Q 5 :

Current passing through a wire as function of time is given as $I$ (t) = 0.02 t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is: [2025]

Q 6 :

A uniform metallic wire carries a current of 2 A, when a 3.4 V battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{- 3} kg$ , density is $8.92 \times 10^{3} {kg/m}^{3}$ and resistivity is $1.7 \times 10^{- 8} Ω -m$ . The length of the wire is [2023]

Q 7 :

The resistance of a wire is $5 Ω$ . Its new resistance in ohm, if stretched to 5 times of its original length, will be [2023]

Q 8 :

The charge flowing in a conductor changes with time as $Q (t) = α t - β t^{2} + γ t^{3},$ where $α$ , $β$ and $γ$ are constants. Minimum value of current is [2023]

Q 10 :

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor [2023]

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]

Q 12 :

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

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]

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]

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Topic Question Set

Q 1 : The electric current through a wire varies with time as I=I0+βt where I0=20A and β=3A/s. The amount of electric charge crossed through a section of the wire in 20 sec is [2024]

Q 2 : The current in a conductor is expressed as I=3t2+4t3, where I is in Ampere and t is in second. The amount of electric charge that flows through a section of the conductor during t=1s to t=2s is _________ C. [2024]

Q 3 : Which of the following resistivity (ρ) v/s temperature (T) curve is most suitable to be used in wire bound standard resistors? [2025]

Q 4 : The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have [2025]

Q 5 : Current passing through a wire as function of time is given as I(t) = 0.02 t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is: [2025]

Q 6 : A uniform metallic wire carries a current of 2 A, when a 3.4 V battery is connected across it. The mass of the uniform metallic wire is 8.92×10-3 kg, density is 8.92×103 kg/m3 and resistivity is 1.7×10-8 Ω-m. The length of the wire is [2023]

Q 7 : The resistance of a wire is 5 Ω. Its new resistance in ohm, if stretched to 5 times of its original length, will be [2023]

Q 8 : The charge flowing in a conductor changes with time as Q(t)=αt-βt2+γt3, where α, β and γ are constants. Minimum value of current is [2023]

Q 10 : In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor [2023]

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×10-3 Ω. If the resistivity of the material is 2.4×10-8 Ω m, the value of n is ________. [2023]

Q 12 : If a copper wire is stretched to increase its length by 20%, the percentage increase in resistance of the wire is ______ %. [2023]

Q 13 : A current of 2 A flows through a wire of cross-sectional area 25.0 mm2. The number of free electrons in a cubic meter are 2.0×1028. The drift velocity of the electrons is ____ ×10-6ms-1 (given, charge on electron =1.6×10-19 C). [2023]

Q 14 : The number density of free electrons in copper is nearly 8×1028 m-3. A copper wire has its area of cross section =2×10-6 m2 and is carrying a current of 3.2 A. The drift speed of the electrons is _______ ×10-6 ms-1. [2023]

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Q 1 :

The electric current through a wire varies with time as $I = I_{0} + β t$ where $I_{0} = 20 A$ and $β = 3 A / s .$ The amount of electric charge crossed through a section of the wire in 20 sec is [2024]

Q 2 :

The current in a conductor is expressed as $I = 3 t^{2} + 4 t^{3}$ , where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1 s$ to $t = 2 s$ is _________ C. [2024]

Q 3 :

Which of the following resistivity ( $ρ$ ) v/s temperature (T) curve is most suitable to be used in wire bound standard resistors? [2025]

Q 4 :

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have [2025]

Q 5 :

Current passing through a wire as function of time is given as $I$ (t) = 0.02 t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is: [2025]

Q 6 :

A uniform metallic wire carries a current of 2 A, when a 3.4 V battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{- 3} kg$ , density is $8.92 \times 10^{3} {kg/m}^{3}$ and resistivity is $1.7 \times 10^{- 8} Ω -m$ . The length of the wire is [2023]

Q 7 :

The resistance of a wire is $5 Ω$ . Its new resistance in ohm, if stretched to 5 times of its original length, will be [2023]

Q 8 :

The charge flowing in a conductor changes with time as $Q (t) = α t - β t^{2} + γ t^{3},$ where $α$ , $β$ and $γ$ are constants. Minimum value of current is [2023]

Q 10 :

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor [2023]

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]

Q 12 :

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

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]

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]