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.

Voltage is the work per unit charge, representing the electrical potential difference.

Current is the rate of charge flow, measured in Amperes (A). Expressed as: $$I = \frac{dQ}{dt}$$

Resistance is the opposition to current flow in a circuit, measured in Ohms (Ω).

Current Density is a vector quantity that relates the current to the electric field (E) and material properties. It's given by: $$J = \frac{I}{A} = \sigma E$$

Resistivity is a material property that describes how much it resists current flow.

Electric Power is the rate at which electrical energy is used, measured in Watts (W).