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Circuit and electromagnetism basics

Learn the electrical fundamentals behind electronics — Ohm's and Kirchhoff's laws, Thevenin's theorem, AC impedance and resonance, RC and RL transients, and electromagnetic induction — with multiple-choice questions.

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Circuit and electromagnetism basics: key points

Circuit analysis rests on Ohm's law and Kirchhoff's current and voltage laws. With series and parallel combinations, voltage and current dividers, Thevenin's theorem and superposition, even complex circuits can be reduced to simple equivalents for calculation.

In AC circuits, the reactances of inductors and capacitors change with frequency and create phase differences between voltage and current. Impedance, resonance, power factor, transient time constants and the underlying laws of electric fields, magnetic fields and induction are the foundation of every field that deals with electronic circuits, not just semiconductors.

All Circuit and electromagnetism basics questions (50)
  1. What is the combined resistance of three resistors, 100 Ω, 200 Ω and 300 Ω, connected in series?
  2. What is the combined resistance of a 6 Ω and a 3 Ω resistor connected in parallel?
  3. Which correctly states Kirchhoff's voltage law (second law)?
  4. When a DC voltage of 10 V is applied across a 100 Ω resistor, how much power does the resistor dissipate?
  5. Which is closest to the peak value (amplitude) of a sinusoidal AC voltage with an RMS value of 100 V?
  6. What is the frequency of a sinusoidal AC voltage whose instantaneous value is v = 10 sin(100πt) [V]? (t in seconds)
  7. When a sinusoidal AC voltage is applied to an ideal capacitor, which correctly describes the phase relationship between the current and the voltage?
  8. In an AC circuit, with active power P [W] and apparent power S [VA], which expression gives the power factor?
  9. What is the time constant of an RC circuit with a resistor R = 1 kΩ and a capacitor C = 10 µF in series?
  10. A DC voltage E is applied through a resistor R to an uncharged capacitor. Which correctly describes the capacitor immediately after the voltage is applied?
  11. How does the magnitude of the electrostatic (Coulomb) force between two point charges in vacuum change if the distance is doubled without changing the charges?
  12. When a direct current flows in a long straight wire, which correctly describes the shape and direction of the magnetic field around it?
  13. In a parallel-plate capacitor, if the plate area is doubled and the plate spacing is halved, by what factor does the capacitance change? (The dielectric between the plates is unchanged.)
  14. An AC voltage of 100 V (RMS) is applied to the primary of an ideal transformer with 1000 primary turns and 100 secondary turns. What is the secondary voltage (RMS)?
  15. When the magnetic flux through a coil changes, an EMF is induced in the coil (electromagnetic induction). Which determines the magnitude of this induced EMF?
  16. Resistors R1 = 2 kΩ and R2 = 1 kΩ are connected in series, in that order from the positive terminal, across a 12 V DC supply (the other end of R2 goes to the negative terminal). What is the voltage across R2? (No current is drawn from the output.)
  17. A 10 Ω and a 20 Ω resistor are connected in parallel, and a total current of 3 A flows into the combination. What current flows through the 20 Ω resistor?
  18. Resistors R1 = 6 kΩ and R2 = 4 kΩ are connected in series across a 10 V DC voltage source (zero internal resistance), with the output terminals across R2. Which is the correct Thevenin equivalent (Vth and Rth) seen from the output terminals?
  19. Which Norton equivalent (current source and resistor) is equivalent to a voltage source with an EMF of 12 V and an internal resistance of 4 Ω?
  20. A load resistor RL is connected to a DC source with an EMF of 10 V and an internal resistance of 50 Ω. As RL is varied, what is the maximum power dissipated in the load?
  21. A 10 V voltage source V1 connects to node A through R1 = 10 Ω, a 5 V voltage source V2 connects to the same node A through R2 = 10 Ω, and a resistor R3 = 10 Ω connects node A to ground. The negative terminals of both sources are grounded. What is the voltage at node A?
  22. Across a 10 V DC supply, two branches are connected in parallel: R1 = 1 kΩ in series with R2 = 1 kΩ, and R3 = 1 kΩ in series with R4 = 1.5 kΩ (R1 and R3 on the positive side). What is the magnitude of the voltage between the R1–R2 junction and the R3–R4 junction? (Ignore any current drawn by the measurement.)
  23. For a wire of circular cross-section, made of the same material and with the same length, how does the resistance change if the diameter is doubled? (Same temperature.)
  24. Which is closest to the reactance of a 1 µF capacitor at a frequency of 1 kHz?
  25. What is the magnitude of the impedance of a circuit with a resistor R = 30 Ω in series with a coil of reactance XL = 40 Ω? (Ignore the coil's resistance.)
  26. Which is closest to the resonant frequency of a series resonant circuit with L = 1 mH and C = 10 nF?
  27. Which correctly describes a series RLC circuit driven by a sinusoidal voltage at its resonant frequency?
  28. When a sinusoidal AC voltage of 100 V RMS is applied to a 50 Ω resistor, what is the average power dissipated?
  29. An AC load has an active power of 800 W and an apparent power of 1000 VA. What is its reactive power? (Sinusoidal voltage and current.)
  30. In a balanced three-phase system with a Y (star) connection, the phase voltage (between each phase and the neutral) is 100 V RMS. Which is closest to the line-to-line voltage (RMS)?
  31. What is generally done to improve the power factor of a circuit containing an inductive load such as a motor?
  32. What is the time constant of an RL circuit with a coil of inductance L = 10 mH in series with a resistor R = 100 Ω?
  33. A resistor R = 5 Ω and a coil (winding resistance negligible) are connected in series to a 10 V DC source, and the switch is closed. Which pair gives the current immediately after closing the switch and after a long time?
  34. A capacitor charged to 10 V is discharged through a resistor. Which is closest to the capacitor voltage after a time equal to the time constant τ?
  35. How much energy is stored in a 10 µF capacitor charged to 10 V?
  36. How much energy is stored in a coil of inductance 2 mH carrying a DC current of 3 A?
  37. A straight wire 10 cm long is placed perpendicular to a uniform magnetic field of flux density 0.5 T and carries a current of 2 A. What is the magnitude of the force on the wire?
  38. A voltage of 100 V is applied between parallel-plate electrodes 1 mm apart. What is the electric field strength between them? (Assume a uniform field.)
  39. In air, a current of 10 A flows in a long straight wire. Which is closest to the magnetic flux density at a point 10 cm from the wire? (μ0 = 4π×10⁻⁷ H/m; take the permeability of air as μ0.)
  40. A bar magnet's north pole is moved toward a coil whose ends are connected to form a closed circuit. Which correctly describes the direction of the induced current in the coil?
  41. In a voltage divider made of two 10 kΩ resistors in series across a 10 V DC supply, a 10 kΩ load resistor is connected in parallel with the lower (ground-side) resistor. Which is closest to the output voltage (across the lower resistor)?
  42. For a balanced three-phase load with a line voltage of 200 V, a line current of 10 A and a power factor of 0.8, which is closest to the load's active power (total of all three phases)?
  43. Which is closest to the bandwidth (the difference between the two frequencies at which the current falls to 1/√2 of its resonant value) of a series RLC resonant circuit with R = 10 Ω, L = 1 mH and C = 10 nF?
  44. A DC voltage is applied through a resistor R = 10 kΩ to an uncharged capacitor C = 10 µF. Which is closest to the time for the capacitor voltage to reach 50% of its final value?
  45. An uncharged capacitor C is fully charged from a DC voltage E through a resistor R. Which correctly gives the energy dissipated in the resistor during charging?
  46. A coil and a 10 Ω resistor are connected in series to a 10 V DC source, and a 100 Ω resistor is connected in parallel with the coil. After a long time, a switch disconnects the source and the 10 Ω resistor. What is the magnitude of the voltage across the 100 Ω resistor immediately after disconnection? (Ignore the coil's winding resistance.)
  47. A charged parallel-plate capacitor is disconnected from its source, and the gap between the plates (air, relative permittivity taken as 1) is completely filled with a dielectric of relative permittivity εr. How do the voltage between the plates and the stored energy change?
  48. Two coils with self-inductances L1 = 4 mH and L2 = 9 mH are magnetically coupled with a coupling coefficient k = 0.5. What is the mutual inductance M?
  49. An 8 Ω resistive load is connected to the secondary of an ideal transformer with turns ratio N1:N2 = 10:1. What impedance is seen from the primary side?
  50. A current of 2 A flows in a solenoid 0.5 m long with a radius of 1 cm and 500 turns (treat it as sufficiently long). Which is closest to the magnetic flux density near the center inside it? (In vacuum, μ0 = 4π×10⁻⁷ H/m.)

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