Resistance, capacitance, and RC
Ohm's law ties voltage to current, capacitors store charge, and together they set every circuit's timing.
Ohm's law
Across a resistor, current grows in proportion to voltage: V = IR. Resistance grows with the material's resistivity and length and shrinks with cross-section, R = rho*L/A. The power dissipated is P = IV, which becomes I^2 R for a resistor.
V = IRCombinations
Resistors in series add directly; in parallel the reciprocals add, so the pair is always less than the smallest resistor. A capacitor stores charge Q = CV and holds energy (1/2)CV^2. Through a resistor it charges or discharges with time constant tau = RC: after one tau it is about 63 percent of the way to its final value.
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}Worked example
A 12 V battery drives two resistors in parallel: 6.0 ohms and 3.0 ohms. The parallel combination is (6.0)(3.0)/(6.0 + 3.0) = 2.0 ohms, so the battery pushes I = 12/2.0 = 6.0 A. Each branch sees the full 12 V: 2.0 A through the 6.0-ohm resistor and 4.0 A through the 3.0-ohm one, summing to 6.0 A as they must.
R_p = \frac{(6.0)(3.0)}{6.0 + 3.0} = 2.0\ \OmegaFlashcard
Ohm's law: voltage equals current times resistance
Check your understanding
A 9.0 V battery drives 3.0 A through a resistor. What power does the resistor dissipate?