Circuits Part 1: Current & Resistance

Current and Voltage

Current is charge flow per time, $I = Q/t$; conventional current points the way positive charge moves. Voltage is energy per charge, $V = W/q$: the push that drives current. Metals conduct with electrons; body fluids conduct with ions moving both ways.

Resistance and Ohm's Law

$V = IR \qquad R = \rho\frac{L}{A}$ Longer wires resist more, thicker wires less, and most metals resist more when hot.

Series, Parallel and Kirchhoff

Series resistors share one current and add: $R_{eq} = R_1 + R_2 + \cdots$. Parallel resistors share one voltage and combine reciprocally, so the equivalent is below the smallest branch. The junction rule conserves charge; the loop rule conserves energy.

Power

$P = IV = I^2R = \frac{V^2}{R}$ In series the larger resistor dissipates more ($I^2R$); in parallel the smaller one does ($V^2/R$).

Key Takeaways

• Series: same current, voltages divide. Parallel: same voltage, currents divide.
• Adding a parallel branch always lowers total resistance and raises total current.
• Collapse networks from the inside out, then walk back out for branch values.
• Pick the power formula that holds the known quantity constant.