Electrical and electronic circuits: DC/AC analysis, components and basic electronics
What the exam tests
DC circuit analysis (Ohm, Kirchhoff, series/parallel, Thévenin), AC steady state (RMS, phasors, impedance, resonance, power factor), and basic electronics (diodes, BJT switching, op-amps, logic interface).
DC rules
- KCL: sum of currents at a node = 0; KVL: sum of voltages around a loop = 0.
- Series: R_eq = ΣR, same current. Parallel: 1/R_eq = Σ1/R, same voltage.
- Voltage divider V_out = V_in R2/(R1+R2) only when unloaded.
- Thévenin: V_th = open-circuit voltage; R_th = resistance seen with sources killed (voltage sources shorted, current sources opened).
- Power P = VI = I²R = V²/R.
AC rules
- v(t) = V_m sin(ωt); V_rms = V_m/√2 for sinusoids.
- Impedance: R, jωL, 1/(jωC). Series RLC: Z = R + j(ωL − 1/ωC). Resonance at ω0 = 1/√(LC); at resonance Z is purely resistive and current is maximum.
- Power: P = VI cosφ; power-factor correction adds parallel capacitance.
- Three-phase: line voltage = √3 × phase voltage in star; line current = √3 × phase current in delta.
Electronics
- Silicon diode: forward drop about 0.7 V; reverse blocking. Zener regulates in reverse breakdown.
- BJT as switch: base current must exceed I_C/h_FE; saturation V_CE about 0.2 V.
- Op-amp ideal rules: no input current, V+ = V− with negative feedback. Inverting gain = −R_f/R_in; non-inverting = 1 + R_f/R_in.
Worked example
A 12 V source feeds R1 = 4 kΩ in series with a parallel pair R2 = 6 kΩ and R3 = 3 kΩ. Parallel: 6||3 = 2 kΩ. Total = 6 kΩ, I = 2 mA. Voltage across the parallel pair = 2 mA × 2 kΩ = 4 V. Current in 6 kΩ = 4/6 = 0.667 mA; in 3 kΩ = 1.333 mA.
Traps
- Using peak voltage instead of RMS in power calculations.
- Adding impedances as scalars.
- Ignoring diode drops.
- Assuming an unloaded divider formula under load.
- Mixing line and phase quantities in three-phase.