Electrical Principles and Circuit Theory
Electrical Principles and Circuit Theory tests the calculations and concepts that underpin every later topic: Ohm's law, power, series and parallel networks, Kirchhoff's laws, alternating current, impedance and three-phase relationships. Expect short numerical questions and questions asking you to predict what happens to current or voltage when a component changes.
Core rules
- V = IR; P = VI = I squared R = V squared / R. Keep units consistent: volts, amps, ohms, watts.
- Series: same current everywhere, voltages add, R total = R1 + R2 + ...
- Parallel: same voltage across each branch, currents add, 1/R total = 1/R1 + 1/R2. For two resistors, R total = (R1 x R2)/(R1 + R2).
- Kirchhoff: current into a node equals current out; the sum of voltage rises equals the sum of drops around a closed loop.
- AC: V rms = V peak / square root of 2, so a 230 V supply has a peak of about 325 V. Inductance and capacitance produce reactance; together with resistance they form impedance Z. Power factor = P/S.
- Three-phase star connection: line voltage = square root of 3 x phase voltage, so 400 V line gives about 230 V phase. In a balanced system the neutral current is zero.
Worked example
A 12 V supply feeds a 4 ohm resistor in series with a parallel pair of 6 ohm and 3 ohm. Parallel pair: Rp = (6 x 3)/(6 + 3) = 18/9 = 2 ohm. Total resistance: 4 + 2 = 6 ohm, so supply current I = 12/6 = 2 A. Voltage across the parallel pair = 2 A x 2 ohm = 4 V; across the 4 ohm resistor = 2 A x 4 ohm = 8 V. Branch currents: 4/6 = 0.67 A and 4/3 = 1.33 A, which add to 2 A. Check: 8 V + 4 V = 12 V.
Traps
- Adding parallel resistances directly instead of using reciprocals.
- Using peak voltage where rms is required, or forgetting the square root of 3 in three-phase work.
- Ignoring power factor on motor loads, or applying it to purely resistive circuits.
- Dropping units or rounding too early in a multi-step calculation.