ECAT — Engineering College Admission Test (UET)

ECAT Physics — Electrostatics and Current Electricity (Set 1)

Take the ECAT Physics — Electrostatics and Current Electricity (Set 1): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…

What this test covers

30 ECAT Physics

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

Q1. Two point charges of 2 μC and 3 μC are 0.3 m apart in air. What force does each exert on the other? (k = 9 × 10⁹ N m² C⁻²)
- A. 0.18 N
- B. 6 N
- C. 0.06 N
- D. 0.6 N ✓
Answer: D. 0.6 N
Explanation: F = kq₁q₂/r² = 9 × 10⁹ × 6 × 10⁻¹²/0.09 = 0.6 N.
Q2. If each of two point charges is doubled and the distance between them is also doubled, the electrostatic force between them:
- A. becomes four times
- B. becomes twice
- C. becomes half
- D. remains the same ✓
Answer: D. remains the same
Explanation: F ∝ q₁q₂/r²: the numerator increases by 4 and r² increases by 4.
Q3. Two identical small conducting spheres carry charges +6 μC and −2 μC and attract each other with force F. They are touched together and returned to the same separation. The new force is:
- A. F/3, attractive
- B. F, repulsive
- C. 4F/3, repulsive
- D. F/3, repulsive ✓
Answer: D. F/3, repulsive
Explanation: After contact each has (6 − 2)/2 = +2 μC. F′/F = (2 × 2)/(6 × 2) = 1/3, and like charges repel.
Q4. What is the electric field intensity at a distance of 0.2 m from a point charge of 4 μC in air? (k = 9 × 10⁹ N m² C⁻²)
- A. 1.8 × 10⁵ N/C
- B. 4.5 × 10⁵ N/C
- C. 9 × 10⁵ N/C ✓
- D. 3.6 × 10⁶ N/C
Answer: C. 9 × 10⁵ N/C
Explanation: E = kq/r² = 9 × 10⁹ × 4 × 10⁻⁶/0.04 = 9 × 10⁵ N/C.
Q5. According to Gauss's law, the total electric flux through a closed surface enclosing a net charge q is:
- A. zero
- B. q/4πε₀
- C. q/ε₀ ✓
- D. qε₀
Answer: C. q/ε₀
Explanation: Φ = q/ε₀, independent of the shape and size of the closed surface.

The other 25 questions

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Q6. A potential difference of 200 V is applied across two parallel plates 4 mm apart. What is the electric field between them?
- A. 800 V/m
- B. 5 × 10⁴ V/m
- C. 5 × 10² V/m
- D. 50 V/m
Q7. How much work is needed to move a charge of 2 μC between two points with a potential difference of 50 V?
- A. 1 × 10⁻⁴ J
- B. 4 × 10⁻⁸ J
- C. 25 × 10⁻⁶ J
- D. 1 × 10⁻² J
Q8. An electron starting from rest is accelerated through a potential difference of 100 V. What kinetic energy does it gain?
- A. 100 J
- B. 1.6 × 10⁻¹⁹ J
- C. 1.6 × 10⁻¹⁷ J
- D. 1.6 × 10⁻²¹ J
Q9. A dielectric of relative permittivity 5 completely fills the space between the plates of a parallel-plate capacitor. Its capacitance becomes:
- A. 25 times
- B. 5 times
- C. 1/5 times
- D. unchanged
Q10. Three identical 6 μF capacitors are joined one after another in series. What is the net capacitance?
- A. 6 μF
- B. 2 μF
- C. 3 μF
- D. 18 μF
Q11. A 4 μF capacitor is charged to 100 V. How much energy is stored in it?
- A. 0.02 J
- B. 4 × 10⁻⁴ J
- C. 0.2 J
- D. 0.04 J
Q12. At the midpoint of the line joining equal and opposite point charges +q and −q:
- A. the potential is zero but the electric field is not zero
- B. both the field and the potential are maximum
- C. the field is zero but the potential is not
- D. both the field and the potential are zero
Q13. Which statement about an equipotential surface is correct?
- A. Work is needed to move a charge along it
- B. Two equipotential surfaces can intersect
- C. The electric field is parallel to it
- D. The electric field is everywhere perpendicular to it
Q14. A charged oil droplet of weight 4.8 × 10⁻¹⁴ N stays suspended in a uniform upward electric field of 1 × 10⁵ N/C. How many excess electrons does it carry? (e = 1.6 × 10⁻¹⁹ C)
- A. 3
- B. 4
- C. 6
- D. 2
Q15. A 10 μF capacitor is charged through a 500 kΩ resistor. After about how long does it reach 63% of its final charge?
- A. 2 s
- B. 50 s
- C. 5 s
- D. 0.5 s
Q16. A charge of 120 C flows through a wire in 1 minute. What is the current?
- A. 7200 A
- B. 2 A
- C. 0.5 A
- D. 120 A
Q17. How many electrons pass a point in a wire each second when it carries a current of 1.6 A? (e = 1.6 × 10⁻¹⁹ C)
- A. 10¹⁸
- B. 1.6 × 10¹⁹
- C. 2.56 × 10⁻¹⁹
- D. 10¹⁹
Q18. A uniform wire of resistance R is stretched to twice its original length (volume unchanged). Its new resistance is:
- A. R
- B. 4R
- C. 2R
- D. R/2
Q19. What is the resistance of a copper wire 2 m long with cross-sectional area 1 mm²? (resistivity of copper = 1.7 × 10⁻⁸ Ω m)
- A. 0.034 Ω
- B. 3.4 Ω
- C. 0.0085 Ω
- D. 0.34 Ω
Q20. A platinum resistance thermometer reads 10 Ω at 0 °C and 12 Ω when dipped in a hot liquid. If α = 0.004 K⁻¹, what is the temperature of the liquid?
- A. 20 °C
- B. 40 °C
- C. 50 °C
- D. 80 °C
Q21. Resistors of 4 Ω and 6 Ω are connected in series across a 20 V supply. What is the potential difference across the 6 Ω resistor?
- A. 10 V
- B. 12 V
- C. 8 V
- D. 20 V
Q22. What is the equivalent resistance of 6 Ω and 3 Ω resistors connected in parallel?
- A. 2 Ω
- B. 0.5 Ω
- C. 4.5 Ω
- D. 9 Ω
Q23. A battery of emf 12 V and internal resistance 1 Ω is connected to a 5 Ω resistor. What is the terminal potential difference of the battery?
- A. 12 V
- B. 11 V
- C. 10 V
- D. 2 V
Q24. A source of emf E and internal resistance r delivers maximum power to an external resistor R when:
- A. R = 2r
- B. R is very large
- C. R = 0
- D. R = r
Q25. What is the resistance of the filament of a bulb rated 100 W, 220 V when it is operating normally?
- A. 22000 Ω
- B. 484 Ω
- C. 2.2 Ω
- D. 242 Ω
Q26. The rule that the algebraic sum of emfs around any closed loop equals the algebraic sum of the IR potential drops in that loop follows from the conservation of:
- A. charge
- B. mass
- C. energy
- D. momentum
Q27. A Wheatstone bridge is balanced with P = 10 Ω, Q = 20 Ω and R = 15 Ω. What is the value of the fourth resistance S?
- A. 30 Ω
- B. 13.3 Ω
- C. 7.5 Ω
- D. 45 Ω
Q28. On a potentiometer, a standard cell of emf 1.5 V balances at 75 cm. An unknown cell balances at 60 cm. What is the emf of the unknown cell?
- A. 1.2 V
- B. 1.25 V
- C. 0.9 V
- D. 1.875 V
Q29. A 2 kW heater is used for 3 hours. At Rs 50 per unit (kWh), what is the cost of the energy used?
- A. Rs 150
- B. Rs 30
- C. Rs 300
- D. Rs 600
Q30. A hollow metal sphere carries a positive charge on its surface. What is the electric field at a point inside the sphere?
- A. zero
- B. directed radially outward and decreasing towards the centre
- C. the same as at its surface
- D. maximum at the centre