Current, resistance, and circuits

Current is charge flow and resistance is a material response

Electric current measures charge crossing a surface per time. A resistor converts organized electrical energy into thermal energy while imposing a voltage-current relation.

Build Ohm’s law as a model

Define I = dQ/dt. For an ohmic material, experiments show voltage drop proportional to current: V = IR. In a uniform wire, microscopic conduction gives R = ρ_e L/A, where ρ_e is resistivity, L length, and A cross-sectional area. Thus longer wires resist more and thicker wires resist less.

A 12 V supply across 6 Ω gives I = 2 A and power P = VI = 24 W. A 2 m copper wire with area 1 mm² and resistivity 1.7×10⁻⁸ Ω·m has R = 0.034 Ω, illustrating why short thick conductors carry large currents.

Ohm’s law is not universal

Incandescent filaments, diodes, motors, and electrolytes can have nonlinear V–I curves. Use V = IR only after checking whether resistance is approximately constant over the operating range.

Work it: A 24 V pump-control branch draws 3 A. Calculate resistance and power. If the wire resistance adds 0.4 Ω, find the voltage lost and power dissipated in the wire.