Electric Current and Current Density, Drift Velocity and Relaxation Time PYQs: JEE Mains Physics

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1. 1. A cylindrical conductor of length 2m and area of cross-section \( 0.2\,mm^{2} \) carries an electric current of 1.6 A when its ends are connected to a 2V battery. Mobility of electrons in the conductor is \( \alpha\times10^{-3} m^{2}/V.s \). The value of \( \alpha \) is:
   (electron concentration \( =5\times10^{28}/m^{3} \) and electron charge \( =1.6\times10^{-19} C \)) 2026 Easy
2. 2. A parallel plate capacitor of area \(A=16 \mathrm{~cm}^2\) and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area \(\mathrm{A}_0=3.2 \mathrm{~cm}^2\) inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through \(\mathrm{A}_0\) is ________ mA . 2025 Medium
3. 3. Current passing through a wire as function of time is given as \(\mathrm{I}(\mathrm{t})=0.02 \mathrm{t}+0.01 \mathrm{~A}\). The charge that will flow through the wire from \(t=1 s\) to \(t=2 s\) is : 2025 Medium
4. 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 Easy
5. 5. 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 \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\). 2024 Hard
6. 6. The electric current through a wire varies with time as \(I=I_0+\beta t\). where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is : 2024 Hard
7. 7. A current of \(2\,A\) flows through a wire of crosssectional 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 Easy
8. 8. In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor 2023 Medium
9. 9. The charge flowing in a conductor changes with time as \(Q ( t )=\alpha t -\beta t ^2+\gamma t ^3\). Where \(\alpha, \beta\) and \(\gamma\) are constants. Minimum value of current is : 2023 Medium
10. 10. The drift velocity of electrons for a conductor connected in an electrical circuit is \(V _{ d }\). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be 2023 Easy
11. 11. 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 Easy
12. 12. \(A\). The drift velocity of electrons decreases with the increase in the temperature of conductor. \(B\). The drift velocity is inversely proportional to the area of cross-section of given conductor. \(C\). The drift velocity does not depend on the applied potential difference to the conductor. \(D\). The drift velocity of electron is inversely proportional to the length of the conductor. \(E\). The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below: 2022 Hard
13. 13. The current density in a cylindrical wire of radius \(4 \; mm\) is \(4 \times 10^{6} \; Am ^{-2}\). The current through the outer portion of the wire between radial distance \(\frac{R}{2}\) and \(R\) is \(\dots \; \pi A .\) 2022 Medium
14. 14. The current density in a cylindrical wire of radius \(r=4.0 \,mm\) is \(1.0 \times 10^{6} \,A / m ^{2}\). The current through the outer portion of the wire between radial distances \(r / 2\) and \(r\) is \(x \pi A\); where \(x\) is .......... 2022 Hard
15. 15. A current of \(10\, A\) exists in a wire of crosssectional area of \(5\, mm ^{2}\) with a drift velocity of \(2 \times 10^{-3}\, ms ^{-1}\). The number of free electrons in each cubic meter of the wire is .......... 2021 Medium
16. 16. A current of \(5\; {A}\) is passing through a non-linear magnesium wire of cross-section \(0.04\; {m}^{2}\). At every point the direction of current density is at an angle of \(60^{\circ}\) with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is ....\({V} / {m}\) (Resistivity of magnesium is \(\rho=44 \times 10^{-8}\, \Omega m\)) 2021 Hard
17. 17. A current through a wire depends on time as \(i =\alpha_{0} t +\beta t ^{2}\) where \(\alpha_{0}=20 A / s\) and \(\beta=8 As ^{-2} .\) Find the charge crossed through a section of the wire in \(15 \,s\) (in \(C\)) 2021 Medium
18. 18. A cylindrical wire of radius \(0.5 \,mm\) and conductivity \(5 \times 10^{7}\, S / m\) is subjected to an electric field of \(10 \,mV / m .\) The expected value of current in the wire will be \(x ^{3} \,\pi mA\). The value of \(x\) is ...... 2021 Medium
19. 19. For the circuit shown, the value of current at time \({t}=3.2\, {s}\) will be ...... \({A}\). [Voltage distribution \(V(t)\) is shown by Fig. \((1)\) and the circuit is shown in Fig. \((2)\)]
    2021 Hard
20. 20. In the given figure, a battery of emf \(E\) is connnected across a conductor \(P Q\) of length \('Y'\) and different area of cross-sections having radii \(r_{1}\) and \(r_{2}\left(r_{2}\,<\,r_{1}\right)\). Choose the correct option as one moves from \(P\) to \(Q\) :
    2021 Hard
21. 21. A current of \(5\, A\) passes through a copper conductor (resistivity \(= 1.7\times10^{-8}\,\Omega \,m\)) of radius of cross-section \(5\, mm\). Find the mobility of the charges if their drift velocity is \(1.1\times10^{-3}\, m/s\) ................ \(m^2/Vs\) 2019 Medium
22. 22. Drift speed of electrons, when \(1.5\, A\) of current flows in a copper wire of cross section \(5\, mm^2\), is \(v\). If the electron density in copper is \(9 \times 10^{28}\, m^3\) the value of \(v\) in \(mm/s\) is close to (Take charge of electron to be \(= 1.6 \times 10^{-19}\, C\)) 2019 Medium
23. 23. The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure What is the value of current at \(t = 4\,s\) ? ............... \(\mu  A\)
    2019 Easy
24. 24. A copper rod of cross-sectional area \(A\) carries a uniform current \(I\) through it. At temperature \(T\), if the volume charge density of the rod is \(\rho \), how long will the charges take to travel a distance \(d\) ? 2018 Medium
25. 25. When \(5\ V\) potential difference is applied across a wire of length \(0.1\ m\), the drift speed of electrons is \(2.5 \times 10^{-4}\) \(ms^{-1}\) . If the electron density in the wire is \(8 \times 10^{28}\) \(m^{-3}\) the resistivity of the material is close to 2015 Medium

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