ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electrostatics and Current Electricity (Set 4): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. Two point charges +q and +4q are 3 m apart. The point on the line joining them where the net electric field is zero is
Answer: C. 1 m from +q
Explanation: Fields cancel where q/x² = 4q/(3 − x)², so 3 − x = 2x and x = 1 m from the smaller charge.
Q2. Charges +q, +q, −q and −q are placed in order at the four corners of a square of side a (so the two +q charges are adjacent). At the centre of the square
Answer: A. V = 0 and E = 4√2 kq/a²
Explanation: Distances to the corners cancel in V (two + and two −). Each charge gives a field 2kq/a² at the centre; the two pairs of fields add along the same direction: 4 × 2kq/a² × cos45° = 4√2 kq/a².
Q3. A large flat insulating sheet carries uniform surface charge density 8.85 μC/m². The electric field near the sheet (ε₀ = 8.85 × 10⁻¹² C²/N m²) is
Answer: D. 5 × 10⁵ N/C
Explanation: For an infinite sheet E = σ/2ε₀ = (8.85 × 10⁻⁶)/(2 × 8.85 × 10⁻¹²) = 5 × 10⁵ N/C.
Q4. A 2 μC charge is moved by the electric field from point A at 100 V to point B at −50 V. The work done by the field is
Answer: B. 300 μJ
Explanation: W = q(V_A − V_B) = 2 μC × 150 V = 300 μJ (positive: the charge moves to lower potential).
Q5. A 2 μF capacitor is charged to 100 V and then disconnected from the supply. A dielectric slab of constant 4 fills the space between its plates. The energy stored becomes
Answer: D. 2.5 mJ
Explanation: Initially U = ½CV² = 10 mJ. With the supply disconnected Q is constant and C becomes 4C, so U = Q²/2C falls to ¼: 2.5 mJ.
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Q6. A 6 μF and a 3 μF capacitor in parallel are connected in series with an 18 μF capacitor, and 90 V is applied across the whole combination. The potential difference across the 18 μF capacitor is
Q7. A 4 μF capacitor charged to 100 V is connected across an uncharged 6 μF capacitor. The energy lost in the process is
Q8. A capacitor C = 5 μF is charged through a resistance R = 2 MΩ from a battery. After 20 s the charge on it is about what percentage of its final value?
Q9. A copper wire of cross-section 2 mm² carries 3.4 A. The free-electron density is 8.5 × 10²⁸ m⁻³ and e = 1.6 × 10⁻¹⁹ C. The drift speed of the electrons is
Q10. A wire is uniformly stretched (its volume staying constant) until its length increases by 50%. The percentage increase in its resistance is
Q11. A coil has resistance 50 Ω at 0 °C and 70 Ω at 100 °C. Assuming linear variation, its resistance at 150 °C is
Q12. A uniform wire of resistance 12 Ω is bent into a circle. The resistance between two points that divide the circumference in the ratio 1 : 2 is
Q13. Two identical cells, each of emf 1.5 V and internal resistance 1 Ω, are joined in parallel across a 2 Ω resistor. The current in the resistor is
Q14. A cell of emf 10 V and internal resistance 1 Ω drives current through a 4 Ω external resistor. The percentage of the total power produced by the cell that is wasted as heat inside the cell is
Q15. A 60 W, 120 V bulb and a 100 W, 120 V bulb are connected in series across a 120 V supply. The total power drawn is
Q16. A 40 W bulb is used for 8 hours every day for 30 days. If electricity costs Rs 20 per unit (kWh), the cost is
Q17. A 12 V cell of internal resistance 2 Ω and a 6 V cell of internal resistance 1 Ω are connected in parallel (like poles together) across a 2 Ω resistor. The current through the resistor is
Q18. A potentiometer wire of length 10 m and resistance 10 Ω is connected in series with a 10 Ω resistor and a 2 V driver cell of negligible internal resistance. A cell is balanced at 6.5 m. Its emf is
Q19. An electron starting from rest is accelerated through a potential difference of 200 V (e = 1.6 × 10⁻¹⁹ C, m = 9.1 × 10⁻³¹ kg). Its final speed is about
Q20. An oil drop of mass 1.44 × 10⁻¹⁴ kg is held stationary between horizontal plates by an upward electric field of 3 × 10⁵ V/m (g = 10 m/s², e = 1.6 × 10⁻¹⁹ C). The number of excess electrons on the drop is
Q21. A point charge q is placed at one corner of a cube. The electric flux through one of the three faces that do not touch the charge is
Q22. The capacitance of an isolated conducting sphere of radius 9 cm in air (1/4πε₀ = 9 × 10⁹ N m²/C²) is
Q23. A 2 μC charge and a −3 μC charge are 0.6 m apart in vacuum. The electric potential energy of the pair is
Q24. A thin conducting spherical shell of radius R carries charge Q. At its centre the electric field and electric potential (zero at infinity) are, respectively
Q25. An alpha particle (charge 2e, e = 1.6 × 10⁻¹⁹ C) lies between two parallel plates 2 mm apart with a potential difference of 200 V. The electric force on it is
Q26. A 1 kW heater with 70% efficiency heats 2 kg of water from 20 °C to 70 °C (specific heat 4200 J/kg K). The time taken is
Q27. Two wires of the same material, of lengths L and 2L and radii r and 2r, are joined in series to a battery. The ratio of the drift speeds of electrons in the first to the second wire is
Q28. The electric field in air just before breakdown is 3 × 10⁶ V/m. The energy density of the field (ε₀ = 8.85 × 10⁻¹² C²/N m²) is about
Q29. A 4 Ω resistor is in series with a parallel pair of 6 Ω and 3 Ω resistors, and a 12 V ideal battery is connected across the arrangement. The current through the 6 Ω resistor is
Q30. Two identical small metal spheres carry charges +6q and −2q and attract each other with force F at a fixed separation. They are touched together and returned to the same separation. The new force is