Use the formula: $$R = \rho \frac{L}{A}$$

Use the formula: $$P = IV$$. You can also use $$P = I^2R = \frac{V^2}{R}$$ if resistance is known.

Add the individual resistances: $$R_{eq} = R_1 + R_2 + R_3 + ...$$

1. Find the reciprocal of each resistance. 2. Add the reciprocals. 3. Take the reciprocal of the sum: $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$$

Ohm's Law relates voltage, current, and resistance: $$V = IR$$. It can be rearranged to find any of the three variables if the other two are known: $$I = \frac{V}{R}$$ or $$R = \frac{V}{I}$$

Increasing the length increases the resistance.

Increasing the cross-sectional area decreases the resistance.

The current doubles (Ohm's Law: V=IR).

The total resistance increases.

The total resistance decreases.

Increasing temperature typically increases resistivity.

The rate of charge flow, measured in Amperes (A). I = dQ/dt

The average velocity of charge carriers (e.g., electrons) due to an electric field.

A vector quantity that relates current to the electric field and material properties. J = I/A = σE

The opposition to current flow in a circuit, measured in Ohms (Ω).

A material property that describes how much it resists current flow.

The rate at which electrical energy is used, measured in Watts (W). P = IV