Unified Tertiary Matriculation Examination · Physics and Chemistry

Electricity, Magnetism and Modern Physics

35 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 35 questions

  1. Calculate the electrostatic force of attraction between two point charges of +2.0 μC and -4.0 μC separated by a distance of 0.20 m in a vacuum. (Coulomb constant k = 9.0 × 10⁹ N·m²/C²)
  2. Determine the electric field intensity at a distance of 0.30 m from an isolated positive point charge of 5.0 nC in air. (Take k = 9.0 × 10⁹ N·m²/C²)
  3. A parallel-plate capacitor has plates of area 0.040 m² separated by a vacuum gap of 2.0 mm. Calculate its capacitance. (Permittivity of free space ε0 = 8.85 × 10⁻¹² F/m)
  4. Two capacitors of capacitances 4.0 μF and 6.0 μF are connected in series across a direct current voltage supply. What is the equivalent capacitance of this combination?
  5. A 10 μF capacitor is charged to a potential difference of 200 V. Calculate the total electrostatic energy stored in the capacitor.
  6. A chemical cell of electromotive force (emf) 1.50 V and internal resistance 0.50 Ω is connected across an external resistor of 2.50 Ω. Calculate the terminal potential difference across the cell.
  7. A cylindrical resistance wire of length 2.0 m and cross-sectional area 5.0 × 10⁻⁷ m² has an electrical resistance of 4.0 Ω. Calculate the electrical resistivity of the wire material.
  8. In a meter bridge experiment, a balance point is obtained at 40 cm from the zero end when a known resistor of 6.0 Ω is placed in the right gap. What is the value of the unknown resistance in the left…
  9. Kirchhoff's first law (current law at an electrical junction) is a direct consequence of which fundamental physical conservation principle?
  10. An electric heating element rated at 2,000 W is designed to operate on a 200 V mains electrical supply. What is the operating electrical resistance of the element?
  11. A consumer operates four 100 W incandescent lamps for 5.0 hours daily over a 30-day billing month. If electrical energy costs ₦50 per kilowatt-hour (kWh), calculate the total monthly electricity cost…
  12. A proton with a charge of 1.6 × 10⁻¹⁹ C travels at 2.0 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.50 T. What magnetic force acts on the proton?
  13. A straight wire of length 0.50 m carries an electric current of 4.0 A at an angle of 30° to a uniform magnetic field of flux density 0.80 T. Calculate the magnetic force exerted on the wire.
  14. A magnetic flux passing through a stationary coil of 200 turns changes uniformly from 0.08 Wb to 0.02 Wb in 0.15 seconds. Calculate the magnitude of the electromotive force induced in the coil.
  15. An ideal step-down transformer has 1,200 turns in its primary coil and 60 turns in its secondary coil. If the primary alternating voltage is 240 V, what is the output voltage from the secondary coil?
  16. A transformer connected to a 240 V mains supply draws an input current of 0.50 A. If the secondary coil delivers a current of 4.0 A at 24 V to a resistive load, what is the electrical efficiency of th…
  17. An inductor of self-inductance 0.20 H is connected across an alternating current voltage source of frequency 50 Hz. Calculate the inductive reactance of this inductor. (Take π ≈ 3.142)
  18. In an alternating current series RLC circuit, electrical resonance occurs when which condition is satisfied?
  19. Which sequence correctly arranges electromagnetic waves in order of strictly decreasing frequency (highest frequency to lowest frequency)?
  20. The work function of a certain photosensitive metallic surface is 2.40 eV. What is the threshold frequency of light capable of liberating photoelectrons from this metal? (Planck constant h = 6.63 × 10…
  21. Monochromatic ultraviolet light of energy 4.50 eV strikes a metal cathode whose work function is 2.80 eV. What is the maximum kinetic energy of the emitted photoelectrons?
  22. In a photoelectric experiment, photoelectrons are emitted with a maximum kinetic energy of 3.2 × 10⁻¹⁹ J. What minimum stopping potential is required to reduce the photocurrent to zero? (Elementary ch…
  23. Calculate the de Broglie wavelength associated with an electron of mass 9.1 × 10⁻³¹ kg traveling at a velocity of 2.0 × 10⁶ m/s. (Planck constant h = 6.63 × 10⁻³⁴ J·s)
  24. According to the Bohr model of the hydrogen atom, what is the energy of a photon emitted when an electron makes a transition from the n = 3 level (-1.51 eV) to the n = 2 level (-3.40 eV)?
  25. A radioactive isotope has an initial activity of 800 counts per second. If its half-life is 4.0 hours, what will its activity be after 12.0 hours?
  26. The half-life of a radioactive sample is 10 days. Calculate its radioactive decay constant λ. (Take ln 2 ≈ 0.693)
  27. During a radioactive decay event, a parent nucleus of Thorium-234 (atomic number 90) emits a beta-minus particle (electron). What is the atomic number and mass number of the resulting daughter nucleus…
  28. Which type of ionizing radiation exhibits the highest specific ionization power along its path through air?
  29. In pure silicon, which pentavalent impurity element is commonly introduced as a donor atom to produce an n-type semiconductor?
  30. When a semiconductor p-n junction is connected in forward bias mode, what happens to the internal depletion region and barrier potential?
  31. What is the function of a full-wave bridge rectifier circuit in an AC-to-DC power supply unit?
  32. Which basic logic gate produces an output of digital 0 (LOW) only when all of its input terminals are simultaneously at digital 1 (HIGH)?
  33. A mass defect of 0.025 u is measured during the formation of a helium nucleus. Calculate the corresponding nuclear binding energy in MeV. (1 u = 931.5 MeV)
  34. Why is high-level nuclear fusion preferred over nuclear fission as an ideal long-term energy source, despite the engineering difficulty of magnetic plasma confinement?
  35. A parallel resonant circuit (tank circuit) contains an inductor of 10 mH and a capacitor of 40 μF. What is the approximate resonant frequency f0 of this circuit?

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