ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Electrostatics and Current Electricity (Set 6): 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. Charges +4 μC and +1 μC are placed 30 cm apart in air. At what distance from the +4 μC charge, on the line joining them, is the net electric field zero?
Answer: D. 20 cm
Explanation: Fields cancel where 4/x² = 1/(0.30 − x)², so x/(0.30 − x) = 2 and x = 20 cm.
Q2. A conducting spherical shell of radius 10 cm carries a charge of 2.0 nC. Taking k = 9×10⁹ N m²/C², the electric potential at a point 5 cm from its centre is
Answer: D. 180 V
Explanation: Inside a conductor the potential is constant and equals the surface value: kQ/R = 9×10⁹×2×10⁻⁹/0.1 = 180 V.
Q3. A very large flat non-conducting sheet carries a uniform surface charge density of 17.7 μC/m² (ε₀ = 8.85×10⁻¹² C²/N m²). The electric field near the sheet, far from its edges, is
Answer: A. 1×10⁶ N/C
Explanation: For a single sheet E = σ/2ε₀ = 17.7×10⁻⁶/(1.77×10⁻¹¹) = 1×10⁶ N/C.
Q4. A parallel-plate capacitor of capacitance 8 pF has its plate gap half filled (by thickness) with a slab of dielectric constant 3, the slab touching one plate and the other half being air. The new capacitance is
Answer: A. 12 pF
Explanation: Two layers in series: 1/C = (d/2)/(ε₀A) + (d/2)/(Kε₀A), which gives C = C₀·2K/(K+1) = 8×6/4 = 12 pF.
Q5. A 6 μF capacitor charged to 100 V is connected, with polarities matching, across an uncharged 3 μF capacitor. The energy lost in the process is
Answer: C. 10 mJ
Explanation: Common voltage = 600 μC/9 μF = 66.7 V. Energy before = 30 mJ, after = 20 mJ, so the loss is 10.0 mJ.
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Q6. A 2 μF and a 4 μF capacitor in series are connected in parallel with a 3 μF capacitor. The equivalent capacitance is
Q7. A capacitor is charged from a 12 V battery through a resistor. At t = 2RC after charging begins, the voltage across the capacitor is (use e⁻² = 0.135)
Q8. A 20 μF capacitor charged to 100 V discharges through a 50 kΩ resistor. The current at t = RC after discharge begins is (use e⁻¹ = 0.368)
Q9. A 10 Ω resistor, a parallel pair of 20 Ω and 30 Ω resistors, and an 8 Ω resistor are connected in series across a 60 V supply. The power dissipated in the 20 Ω resistor is
Q10. A uniform wire of resistance 4 Ω is bent into two equal halves which are then laid side by side and joined at both ends (so the halves are in parallel). The resistance between the joined ends is
Q11. A coil of resistance 50 Ω at 20 °C has a temperature coefficient of resistance 0.004 °C⁻¹. At what temperature is its resistance 65 Ω?
Q12. A 12 V battery of internal resistance 0.5 Ω is being recharged by an external source with a current of 4 A passing through it in the reverse direction. The potential difference across its terminals is
Q13. The largest power that a 6.0 V cell can deliver to any external resistor is 4.5 W. The internal resistance of the cell is
Q14. Two cells, 10 V with internal resistance 2 Ω and 4 V with internal resistance 1 Ω, are connected in parallel (like poles together) across a 1 Ω load. The current through the load is
Q15. A potentiometer wire of length 10 m and resistance 10 Ω is connected in series with a 10 Ω rheostat to a 4 V battery of negligible internal resistance. A cell of emf 1.5 V is balanced on the wire. The balance length is
Q16. An infinitely long straight wire carries a uniform charge of 2.0 μC per metre. Using E = 2kλ/r with k = 9×10⁹ N m²/C², the field at 18 cm from the wire is
Q17. A point charge q is placed at one corner of a cube of side a. The electric flux through one face of the cube that does NOT touch the charge is
Q18. Three equal charges of 3.0 μC are placed at the corners of an equilateral triangle of side 0.30 m (k = 9×10⁹ N m²/C²). The electric potential energy of the system is
Q19. A helium nucleus (charge +2e) is accelerated from rest through a potential difference of 3.0 kV. Its kinetic energy gained, in electron volts, is
Q20. For a charged conductor in electrostatic equilibrium, which statement is correct?
Q21. A 2 μF air capacitor is charged to 12 V and then disconnected from the battery. A dielectric of constant 4 is slipped in to fill the gap completely. The energy stored afterwards is
Q22. A 60 W and a 100 W bulb, both rated for 240 V, are connected in series across a 240 V supply. The ratio of the power dissipated in the 60 W bulb to that in the 100 W bulb is
Q23. A resistor has colour bands yellow, violet, red, silver (digit, digit, multiplier, tolerance: yellow = 4, violet = 7, red = ×10², silver = ±10%). Its resistance lies between
Q24. A current I flows through a copper wire of diameter d. The same current is passed through a copper wire of diameter 2d, with the same free-electron density. The new drift speed is what multiple of the original?
Q25. The current through a wire is a steady 2 A for the first 5 s, and then falls uniformly to zero over the next 5 s. The total charge passed in the 10 s is
Q26. Four point charges +q, +q, −q and −q are placed in that order at the successive corners of a square. At the centre of the square
Q27. A 2 kW heater runs 3 hours every day for 30 days. If electricity costs Rs 40 per kWh (unit), the monthly cost of using the heater is Rs
Q28. Three identical lamps are connected so that two lamps in parallel are in series with the third lamp, across a fixed supply. If one of the two parallel lamps burns out (open circuit), the power dissipated in the series lamp becomes what fraction of its original value? (Treat lamp resistance as constant.)
Q29. A 5 μF capacitor is charged from 0 to 100 V and then from 100 V to 200 V. The extra energy supplied during the second stage is
Q30. The V–I graph of a filament lamp bends so that, at higher voltages, V rises faster than I. This shows that