Fundamentals of Electricity and DC Circuits
1. Fundamentals of Electricity and DC Circuits
This domain tests the definitions of charge, current, potential difference, EMF, resistance and power, and your ability to reduce a DC network using Ohm's law and Kirchhoff's laws. Numerical questions dominate.
Core rules
- Current is the rate of charge flow, I = Q/t, in amperes; one ampere is one coulomb per second.
- Ohm's law: V = IR, valid at constant temperature for ohmic conductors.
- Power: P = VI = I²R = V²/R; energy in kWh = power (kW) × time (h).
- Series: same current, R_total = R1 + R2 + ...; voltage divides in proportion to resistance.
- Parallel: same voltage, 1/R_total = 1/R1 + 1/R2 + ...; the result is always less than the smallest branch.
- KCL: currents entering a node equal currents leaving. KVL: the algebraic sum of voltages round a closed loop is zero.
- EMF is the open-circuit source voltage; terminal voltage = E − Ir, where r is internal resistance.
Worked example
A cell of EMF 12 V and internal resistance 0.5 Ω feeds a 5.5 Ω load. Total resistance = 0.5 + 5.5 = 6 Ω, so I = 12/6 = 2 A. Terminal voltage = E − Ir = 12 − (2 × 0.5) = 11 V, which also equals IR = 2 × 5.5 = 11 V. Load power = I²R = 4 × 5.5 = 22 W; power wasted internally = 4 × 0.5 = 2 W.
Traps
- Reporting EMF where terminal voltage is asked, or ignoring internal resistance.
- Writing 1/R_total = 1/R1 + 1/R2 + ... and then forgetting to invert.
- Mixing mA, kΩ and V without converting to base units.
- Sign errors in KVL when traversing a source from + to −.
- Assuming one parallel branch changes the voltage across the others (it does not with an ideal source).