Current, Resistance, and DC Circuits

Electric Current & Ohm's Law

A wire carries no extra net charge when current flows; electrons drift slowly at about 0.1 mm/s. A bulb lights instantly because the electric push travels near light speed, like water through a hose.

Electric current is the rate of charge flow: $I = \frac{dQ}{dt}$, unit: ampere (A).

Ohm's law links voltage, current, and resistance: $V = IR$.

Resistivity governs material geometry: $R = \rho \frac{L}{A}$, where $\rho$ is material resistivity, $L$ is length, and $A$ is cross-sectional area.

Power dissipated in a resistor is given by: $P = IV = I^2R = \frac{V^2}{R}$.

Circuits, Power & Pitfalls

Joule heating turns electrical energy into heat: $E = Pt = I^2Rt$. This is why power lines use high voltage and low current to minimize losses.

Key insight: Series resistors share identical current, while parallel resistors share identical voltage.

Common pitfall: Current is never "used up" in a circuit. The exact same current returns to the battery; what gets consumed is energy per charge (voltage).