Voltage, current, resistance, power

Why it matters

Every electrical job, from wiring a house to designing a powerThe rate at which energy is converted, for example into heat or light, measured in watts (W). supply, rests on four quantities: voltageThe electrical push: the energy given to each unit of charge between two points, measured in volts (V)., currentThe rate at which charge flows past a point, measured in amperes (A); one amp is one coulomb per second., resistanceHow strongly a material or component opposes current, measured in ohms (Ω). and power. If you can move between them confidently, you can size a resistor, check whether a wire or fuse is big enough, estimate a battery's run time and spot a reading that does not make sense. This lesson gives you the vocabulary and the two formulas you will use in every lesson after it.

The four quantities

Voltage (V, volts) is the electrical "push": the energy given to each unit of charge as it moves between two points. A voltage is always measured between two points, so "the voltage at a wire" really means "the voltage between that wire and some reference", usually the negative terminal or ground.

Current (I, amperes or amps) is the rate at which charge flows past a point. One amp is one coulomb of charge per second. Current is measured through a part of a circuit.

Resistance (R, ohms, Ω) is how strongly a material or component opposes current. Copper wire has very low resistance; a resistor is made to have a known resistance; a lamp filament has a resistance that rises as it heats up.

Power (P, watts) is the rate at which energy is converted, for example into heat or light. One watt is one joule per second.

A water analogy helps at first: voltage is like pressure, current is like flow rate, and resistance is like a narrow pipe. Do not push the analogy too far, but it explains why more push gives more flow and a narrower pipe gives less.

Ohm's law

For a resistor, current is proportional to voltage:

V = I × R      I = V / R      R = V / I

Units must match: volts, amps and ohms. Convert milliamps (mA) to amps by dividing by 1,000, and kilohms (kΩ) to ohms by multiplying by 1,000.

Worked example 1. A 9 V battery is connected across a 470 Ω resistor. What current flows?

I = V / R = 9 / 470 = 0.0191 A ≈ 19 mA

Worked example 2. You measure 2.5 V across a resistor and 5 mA through it. What is its resistance?

R = V / I = 2.5 / 0.005 = 500 Ω

Power

Power is voltage times current:

P = V × I

Substituting Ohm's lawFor a resistor, voltage equals current times resistance: V = I × R. gives two more forms that are handy when you know only two quantities:

P = I² × R        P = V² / R

Worked example 3. In example 1, how much power does the resistor turn into heat?

P = V × I = 9 × 0.0191 = 0.172 W

A standard small resistor is rated 0.25 W, so this one is fine. If the answer had been 0.4 W, you would need a 0.5 W or larger resistor, or it would overheat.

Worked example 4. A 12 V, 36 W lamp. What current does it draw, and what is its hot resistance?

I = P / V = 36 / 12 = 3 A
R = V / I = 12 / 3 = 4 Ω

Energy

Energy is power multiplied by time. Utilities bill in kilowatt-hoursThe unit utilities bill energy in: 1 kWh is 1,000 W used for one hour. (kWh): a 1,000 W heater running for one hour uses 1 kWh. Batteries are rated in amp-hours (Ah) or milliamp-hours (mAh): a 2,000 mAh battery could, in theory, supply 20 mA for 100 hours. Real run times are shorter, because capacity falls at higher currents and the voltage sags as the battery empties.

Common mistakes

• Mixing units. 19 mA is 0.019 A, not 19 A. Write units on every line of a calculation.
• Forgetting that voltage is between two points. A meter has two leads for a reason.
• Using Ohm's law on parts that are not resistors. LEDs, diodes and motors do not have a fixed resistance; you will treat LEDs differently in the breadboard lesson.
• Ignoring power ratings. A calculation can be right and the part can still burn out because its wattage rating is too low.
• Trusting a result that fails a sanity check. A phone charger drawing 300 A is a sign you misplaced a decimal point.

Safety note

The formulas are the same at 9 V and at 480 V, but the danger is not. In this course you practise only on batteries of 9 V or less and in simulators. Work on mains or industrial circuits requires employer or school training, supervision by a qualified person and the right protective equipment.

Recap

• Voltage is push (V), current is flow (A), resistance opposes flow (Ω), power is the rate of energy use (W).
• Ohm's law: V = I × R.
• Power: P = V × I = I² × R = V² / R.
• Convert mA and kΩ before calculating, and check the answer makes sense.

Try it

Open the Do tab and finish a small Ohm's law and power calculator by writing the power formula.