ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electrostatics and Current Electricity (Set 5): 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. A +4 μC charge and a +1 μC charge are fixed 6 cm apart. The point on the line joining them where the net electric field is zero is at a distance from the +4 μC charge of:
Answer: B. 4 cm
Explanation: Zero field between them: 4/x² = 1/(6 − x)², so x = 2(6 − x) and x = 4 cm.
Q2. A sphere with charge +6 μC and an identical sphere with charge −2 μC attract each other with force F when a certain distance apart. The spheres are touched together and returned to the same separation. The force between them is now:
Answer: B. F/3, repulsive
Explanation: Each sphere ends with (6 − 2)/2 = +2 μC. The product of charges changes from 12 to 4, so the magnitude is F/3, and the force is now repulsive.
Q3. Two +5 μC charges are fixed at (−4 cm, 0) and (+4 cm, 0). The electric field at the point (0, 3 cm) has magnitude:
Answer: A. 2.16 × 10⁷ N C⁻¹
Explanation: Each charge is 5 cm from the point: E₁ = kq/r² = 9×10⁹ × 5×10⁻⁶/(0.05)² = 1.8 × 10⁷ N/C. The x-components cancel and the y-components add: 2 × 1.8×10⁷ × (3/5) = 2.16 × 10⁷ N/C.
Q4. An electron (charge 1.6 × 10⁻¹⁹ C, mass 9.1 × 10⁻³¹ kg) starting from rest is accelerated through a potential difference of 45.5 V. Its final speed is:
Answer: A. 4 × 10⁶ m s⁻¹
Explanation: ½mv² = eV: v = √(2 × 1.6×10⁻¹⁹ × 45.5/9.1×10⁻³¹) = √(1.6×10¹³) = 4 × 10⁶ m/s.
Q5. Two equal and opposite point charges are separated by some distance. At the midpoint of the line joining them:
Answer: C. the potential is zero but the field is not zero
Explanation: Potentials +V and −V cancel (scalars), but the fields of the two charges point in the same direction at the midpoint (vectors) and add.
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Q6. Just outside the surface of a charged conductor, the surface charge density is 8.85 × 10⁻⁶ C m⁻² (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²). The electric field there is:
Q7. A conducting sphere of radius 10 cm carries a charge of 10 nC. Taking k = 9 × 10⁹ N m² C⁻², the electric potential at its centre is:
Q8. A spherical surface of radius 2 m encloses point charges of +3 nC, −5 nC and +4 nC, while a +6 nC charge lies outside it. The net electric flux through the sphere is (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²):
Q9. A parallel-plate capacitor stays connected to a battery while the plate separation is doubled, with no change in the plate area or in the medium between them. The energy stored in the capacitor:
Q10. A 4 μF capacitor is connected in parallel with a series combination of 6 μF and 3 μF capacitors, and a 12 V battery is connected across the whole arrangement. The charge on the 3 μF capacitor is:
Q11. A 4 μF capacitor charged to 100 V is disconnected and connected across an uncharged 4 μF capacitor. The energy lost in the process (as heat and radiation) is:
Q12. A 10 μF capacitor charges through a 1 MΩ resistor from a battery (ln 2 = 0.693). The time taken for the capacitor to reach half of its final charge is:
Q13. Three equal point charges of +2 μC are placed at the corners of an equilateral triangle of side 0.6 m (k = 9 × 10⁹ N m² C⁻²). The electrostatic potential energy of the system is:
Q14. Equipotential surfaces in a uniform electric field are drawn at 10 V intervals, and adjacent surfaces are 2 cm apart. The magnitude of the field is:
Q15. A charge is moved from point A to point B along an equipotential surface in an electric field. The work done by the field on the charge is:
Q16. A wire of cross-section 2 mm² carries 8 A. If the free-electron density is 10²⁹ m⁻³, the drift velocity is (e = 1.6 × 10⁻¹⁹ C):
Q17. A wire of resistance 8 Ω is cut into four equal pieces, and the four pieces are connected in parallel. The resistance of the combination is:
Q18. The resistance of a metallic conductor increases linearly with temperature with temperature coefficient α = 4 × 10⁻³ °C⁻¹ (referred to its resistance at 20 °C). At what temperature will its resistance be double its value at 20 °C?
Q19. Four resistors are connected as a balanced Wheatstone bridge: 6 Ω and 12 Ω in series in one arm, and 3 Ω and 6 Ω in series in the other arm (the two arms in parallel between the supply terminals), with a 5 Ω resistor connected between the two midpoints. The equivalent resistance between the supply terminals is:
Q20. A cell of emf 10 V and internal resistance 1 Ω is connected positive-to-positive and negative-to-negative with a cell of emf 4 V and internal resistance 2 Ω. The potential difference across the terminals of the 10 V cell is:
Q21. A battery of emf E and internal resistance r supplies maximum power to an external resistor when its resistance equals r. At that moment, the fraction of the battery's total power that is delivered to the external resistor is:
Q22. A 40 W and a 60 W bulb, both rated for 220 V, are connected in series across a 220 V supply. The ratio of the power actually dissipated in the 40 W bulb to that in the 60 W bulb is:
Q23. A 2 kW heater is used for 3 hours a day. The electricity price is Rs 40 per kW h. The cost for 30 days is:
Q24. In a circuit, the positive terminals of a 12 V cell (in series with 2 Ω) and a 3 V cell (in series with 3 Ω) are both joined to the same junction. A 3 Ω resistor connects this junction to the joined negative terminals. By Kirchhoff's rules, the 3 V cell:
Q25. In a metre bridge, a 10 Ω resistor is in the left gap and an unknown resistor X in the right gap; balance is found at 40 cm from the left end. If R and X are now interchanged, the balance point (from the left end) will be at:
Q26. A 5 m potentiometer wire of resistance 10 Ω is connected in series with a 5 Ω rheostat and a 3 V driver cell of negligible internal resistance. A test cell balances at 2.5 m along the wire. Its emf is:
Q27. A copper wire of length L and radius r, connected across a fixed potential difference, dissipates power P. A second copper wire of length 2L and radius 2r is connected across the same potential difference. The power it dissipates is:
Q28. The current through a conductor falls uniformly from 4 A to zero over 10 s. The total charge that passes through the conductor in this time is:
Q29. The current–voltage graph of a tungsten filament lamp is a curve that becomes less steep as the voltage rises. This shows that:
Q30. Two small charged spheres experience an electrostatic force of 10 N in air. When the same spheres are placed at the same separation in oil of relative permittivity 2.5, the force between them becomes: