ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electrostatics and Current Electricity (Set 7): 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 of 3 μC and 6 μC are 0.3 m apart in air. Taking k = 9 × 10⁹ N m²/C², the force between them is:
Answer: C. 1.8 N
Explanation: F = kq₁q₂/r² = (9 × 10⁹)(18 × 10⁻¹²)/0.09 = 1.8 N.
Q2. A +4 μC and a −4 μC charge are 0.2 m apart in air. Taking k = 9 × 10⁹ N m²/C², the electric field at the midpoint of the line joining them is:
Answer: C. 7.2 × 10⁶ N/C
Explanation: Each charge gives kq/r² = 9 × 10⁹ × 4 × 10⁻⁶/0.01 = 3.6 × 10⁶ N/C in the same direction (towards the negative charge); total = 7.2 × 10⁶ N/C.
Q3. Charges +4q and +q are 3 m apart in vacuum. The point on the line between them where the net electric field is zero is at distance from the +4q charge of:
Answer: D. 2 m
Explanation: Zero field where 4q/x² = q/(3 − x)², giving 2(3 − x) = x, x = 2 m.
Q4. An infinite flat sheet carries a uniform surface charge density of 8.85 μC/m². Taking ε₀ = 8.85 × 10⁻¹² C²/(N m²), the field near it is:
Answer: A. 5 × 10⁵ N/C
Explanation: For a sheet E = σ/2ε₀ = 8.85 × 10⁻⁶/(2 × 8.85 × 10⁻¹²) = 5 × 10⁵ N/C.
Q5. A charge of 8.85 nC is placed at the centre of a cube. Taking ε₀ = 8.85 × 10⁻¹² C²/(N m²), the electric flux through one face of the cube is:
Answer: A. 167 N m²/C
Explanation: Total flux = q/ε₀ = 8.85 × 10⁻⁹/8.85 × 10⁻¹² = 1000 N m²/C; each of the 6 faces gets 1000/6 ≈ 167 N m²/C.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. Taking k = 9 × 10⁹ N m²/C², the electric potential at 0.9 m from a point charge of 5 μC is:
Q7. Three charges of 2 μC each sit at the corners of an equilateral triangle of side 0.6 m. Taking k = 9 × 10⁹ N m²/C², the electric potential energy of the system is:
Q8. An alpha particle (charge +2e) is accelerated from rest through a potential difference of 50 V. Taking e = 1.6 × 10⁻¹⁹ C, its kinetic energy is:
Q9. In a Millikan-type experiment an oil drop of mass 3.2 × 10⁻¹⁵ kg hangs stationary in a vertical field of 1 × 10⁵ N/C. Taking g = 10 m/s² and e = 1.6 × 10⁻¹⁹ C, the drop carries a charge of:
Q10. A parallel-plate capacitor has its plate area doubled and its plate separation tripled (same medium). Its capacitance becomes:
Q11. A 6 μF and a 3 μF capacitor are connected in series, and this combination is connected in parallel with a 4 μF capacitor. The equivalent capacitance is:
Q12. A 2 μF parallel-plate capacitor stays connected to a 12 V battery while a dielectric slab of constant 3 fills the space between the plates. The energy stored afterwards is:
Q13. A 5 μF capacitor charges through a 2 MΩ resistor. The time constant of the circuit is:
Q14. A wire carries electrons so that 3 × 10²⁰ electrons pass a cross-section in 8 s. Taking e = 1.6 × 10⁻¹⁹ C, the current is:
Q15. A wire of resistance 10 Ω is stretched uniformly to twice its original length, its volume remaining constant. Its new resistance is:
Q16. In a metre bridge the known resistance R = 10 Ω is in the left gap and the unknown S in the right gap. The balance point is 40 cm from the left end. The value of S is:
Q17. A 12 V and a 6 V battery of negligible internal resistance are joined in a loop with their like terminals opposing, through resistors of 4 Ω and 2 Ω in series. The current in the loop is:
Q18. A 12 V battery of internal resistance 0.5 Ω is connected to a 5.5 Ω load. The terminal voltage across the battery is:
Q19. A source of emf 10 V and internal resistance 2 Ω supplies a variable external resistance. The maximum power it can deliver to the load is:
Q20. A lamp is marked 220 V, 100 W. Assuming its resistance stays constant, the power it uses when connected to a 110 V supply is:
Q21. A 2 kW heater runs for 3 hours. If electricity costs Rs 30 per unit (1 unit = 1 kWh), the cost is:
Q22. A resistor's colour bands are red, violet, orange and gold in that order (red 2, violet 7, orange ×10³, gold ±5%). Its resistance is:
Q23. A resistor has a resistance of 100 Ω at 0°C and a temperature coefficient of 0.004 °C⁻¹. Taking R = R₀(1 + αΔT), its resistance at 50°C is:
Q24. The resistance of an NTC (negative temperature coefficient) thermistor, as its temperature is raised:
Q25. A potentiometer wire is 10 m long and has a potential gradient of 0.2 V/m. A cell is balanced against 6 m of the wire. Its emf is:
Q26. The work done in moving a charge between two points on the same equipotential surface is:
Q27. Under electrostatic conditions, electric field lines meet the surface of a charged conductor:
Q28. In a uniform electric field, the potential falls from 100 V to 60 V between two points 8 cm apart along a field line. The magnitude of the field is:
Q29. A body carries a charge of −4.8 × 10⁻¹⁸ C. Taking e = 1.6 × 10⁻¹⁹ C, it has:
Q30. A proton (mass 1.6 × 10⁻²⁷ kg, charge 1.6 × 10⁻¹⁹ C) is accelerated from rest through 800 V. Its final speed is: