Current, Resistance & Ohm’s Law

You’ll be able to

Define electric current as the rate of charge flow and identify conventional current direction
Relate voltage, current, and resistance through Ohm’s law
Calculate electrical power dissipated in a resistor

Current is charge in motion

Electric current (I) is the rate at which charge flows past a point: I = Q/t, measured in amperes (1 A = 1 C·s⁻¹). By convention, current is drawn in the direction positive charge would move — from the + terminal of a battery around to the − terminal — even though in a metal wire it is really electrons drifting the opposite way. A battery supplies the voltage (potential difference) that pushes this charge around the circuit, like a pump maintaining pressure in a loop of pipe.

Resistance and Ohm’s law

Resistance (R) measures how strongly a component opposes current, in ohms (Ω). For many materials, current is proportional to the voltage across them — Ohm’s law, V = IR. A larger resistance means less current for the same voltage. Resistance grows with a wire’s length and shrinks with its cross-sectional area (a longer, thinner wire resists more), and depends on the material’s resistivity. Think of it as friction for flowing charge, turning electrical energy into heat.

Current, Ohm’s law, and power

I = Q / t · V = I · R · P = I · V = I² · R = V² / R

Power P is the rate at which the resistor converts electrical energy to heat/light, in watts (W). All three power forms are equivalent — pick the one matching your known quantities.

Worked example

A 12 V battery drives current through a 4.0 Ω resistor. Find the current and the power dissipated.

1.Solve Ohm’s law for current: I = V/R = 12 / 4.0 = 3.0 A.
2.Find power with P = IV = (3.0 A)(12 V) = 36 W.
3.Check with P = I²R = (3.0)²(4.0) = 9 × 4 = 36 W — the same.

Answer: I = 3.0 A and P = 36 W of electrical energy is converted to heat each second.

Tip

The water analogy keeps the roles straight: voltage is the pump pressure, current is the flow rate, and resistance is a narrow constriction in the pipe. More pressure or a wider pipe → more flow.

Checkpoint

A resistor has 12 V across it and carries a current of 3.0 A. What is its resistance?

Checkpoint

A wire carries a steady current of 2.0 A for 10 s. How much charge flows past a point in the wire?

On the exam

Know all three power formulas: P = IV, P = I²R, and P = V²/R. If a problem gives you resistance and voltage but not current, P = V²/R saves a step. They are algebraically identical via Ohm’s law.

Answer the 2 checkpoints as you read.