Electricity and DC Circuits
Current, voltage and resistance
Current I = ΔQ/Δt. Potential difference V = W/Q. Resistance R = V/I. Ohm’s law holds when current is proportional to potential difference at constant temperature. Resistivity ρ gives R = ρL/A. A filament lamp is non-ohmic because its resistance rises as temperature rises.
Series, parallel and Kirchhoff’s laws
In series, current is the same and resistances add. In parallel, voltage is the same and 1/R = 1/R₁ + 1/R₂ + …. Kirchhoff’s first law: current into a junction equals current out. Second law: the sum of potential differences around a closed loop is zero. EMF is the energy transferred per unit charge by the source; terminal voltage is lower than EMF when current flows because of internal resistance: V = E − Ir.
Worked example
A battery of EMF 12 V and internal resistance 0.50 Ω is connected to a 5.5 Ω resistor. Total resistance = 6.0 Ω, so I = 12 ÷ 6.0 = 2.0 A. Terminal voltage = 12 − (2.0 × 0.50) = 11 V. The 1 V difference is the potential difference across the internal resistance, dissipated as thermal energy inside the battery.
Traps
Treating terminal voltage as the EMF; adding parallel resistances directly instead of reciprocals; assuming a filament lamp obeys Ohm’s law; placing an ammeter in parallel or a voltmeter in series; using P = VI when the component is non-ohmic without checking the operating point.