Resistance

Resistance ($R$) measures how strongly a component opposes Current for a given Voltage. For an ohmic component,

$R=\frac{V}{I}$

The unit is the ohm ($\Omega$). A larger resistance gives a smaller current for the same applied voltage. Microscopic picture: mobile charges drift through a material and repeatedly scatter from the lattice, impurities, and thermal motion. The electrical energy lost by the charges becomes internal energy, usually heat.

Ohm’s law is a model, not a definition that every device obeys. Resistors are designed to be approximately ohmic over a useful range. Diodes, lamps, thermistors, batteries, and transistors can have nonlinear $I$-$V$ behaviour.

Power dissipated in a resistor can be written three equivalent ways:

$P=IV=I^{2}R=\frac{V^2}{R}$

Series resistances add because the same current must pass through each component:

$R_{series}=R_1+R_2+\cdots$

Parallel resistances add by conductance because each branch has the same voltage:

$\frac{1}{R_{parallel}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$

Material note: resistance depends on the component geometry and material. For a uniform wire,

$R=\rho \frac{L}{A}$

where $\rho$ is resistivity, $L$ is length, and $A$ is cross-sectional area. Longer wires resist more; thicker wires resist less.

Common mistake: assuming resistance “uses up” current. A resistor converts electrical energy to heat; charge is conserved.