Ohm's law, on a working bench

Set a voltage on the supply, choose a resistor and read the current on the meter. Turn the knobs (drag, scroll or use the arrow keys) and the notes underneath work through the sums with your numbers.

PICKETTECH PS-305 DC bench power supply

0–30 V · 0–3 A · CV/CC

VOLTSSET12.00V

AMPSLIMIT0.012A

VOLTAGE

SET

CURRENT

LIMIT

OUTPUT

CVCC

PICKETTECH DM-10 Multimeter

4000 counts · auto range

DC A 12.00 mA

OFF V⎓ A⎓ Ω

PICKETTECH RS-12 Resistor substitution box

E12 · 10 Ω – 1 MΩ · choose the wattage

RESISTANCE

E12 VALUE

POWER RATING

Cool

CIRCUITI 12.0 mAV_R 12.0 VP 144 mW

Ohm's law, live

Power in the resistor

What the meter is doing

Solve any Ohm's law problem

Fill in any two of voltage, current, resistance and power. The other two are worked out, with the formula used.

Voltage V

Current I

Resistance R

Power P

V = I × R

Tap a letter to cover it. What's left is the formula: side by side means multiply, one above the other means divide.

The ideas behind the numbers

Fourteen short lessons, from what a volt is to why a bench supply has a current limit. Most have a button that sets up the bench to show it.

VVoltageThe push that moves charge

Voltage is the difference in electrical pressure between two points. It is what pushes charge around a circuit, and it is measured in volts (V). A voltage always exists between two points, which is why a meter needs two probes.

Think of the height of a waterfall: the higher the drop, the harder the water hits. A 9 V battery pushes harder than a 1.5 V cell.

Source	Voltage
AA cell	1.5 V
USB port	5 V
Car battery	12 V
Mains (Ireland, UK, EU)	230 V AC

ICurrentHow much charge flows each second

Current is the rate at which charge flows past a point, measured in amps (A). One amp is one coulomb of charge per second. Small electronics work in milliamps: 1 mA = 0.001 A.

In a single loop the current is the same everywhere. It isn't "used up" by the resistor; the energy is.

Worked exampleA phone charger supplies 2 A. In one minute, 2 × 60 = 120 coulombs of charge pass through the cable.

RResistanceHow hard a part resists the flow

Resistance opposes current and turns electrical energy into heat. It is measured in ohms (Ω). A thin, long or poorly conducting path has more resistance than a short, thick copper one.

Resistors come in standard values. The E12 series gives twelve steps per decade: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, then 100, 120 and so on. The resistor box on the bench steps through exactly these.

ΩOhm's lawV = I × R, and its two rearrangements

For a resistor, current is proportional to voltage: double the voltage and the current doubles. The constant that links them is the resistance.

V = I × R · I = V ÷ R · R = V ÷ IUse the triangle: cover the letter you want and the other two show the sum.

Worked example12 V across 470 Ω: I = 12 ÷ 470 = 0.0255 A, which is 25.5 mA.

PPower and resistor ratingsWhy resistors get hot, and burn

Power is the rate energy is used, in watts (W). In a resistor it all becomes heat. There are three ways to work it out, depending on what you know:

P = V × I · P = I² × R · P = V² ÷ R

Every resistor has a power rating. A common through-hole resistor is 0.25 W. Go over it and it overheats, discolours and eventually burns open. Choose a rating at least twice the power you calculate.

Worked example12 V across 100 Ω: P = 12² ÷ 100 = 1.44 W. A 0.25 W resistor would burn; use a 2 W or 5 W part.

≈The water-pipe analogyA picture that makes the three quantities click

Electricity isn't water, but the picture helps:

Electric	Water
Voltage	Pressure (how hard it pushes)
Current	Flow rate (litres per second)
Resistance	A narrow pipe
Power	Work done, like turning a water wheel

More pressure pushes more water through the same pipe. A narrower pipe lets less through at the same pressure. That is Ohm's law.

∥Series and parallel resistorsAdding resistors up the right way

In series (one after another) the current has one path, so the resistances simply add. In parallel (side by side) the current splits, so the total is always lower than the smallest resistor.

Series: R = R1 + R2 + … · Parallel: 1/R = 1/R1 + 1/R2 + …Two in parallel: R = (R1 × R2) ÷ (R1 + R2)

Worked example100 Ω and 220 Ω in parallel: (100 × 220) ÷ 320 = 68.75 Ω.

÷Voltage dividersTwo resistors that make a lower voltage

Two resistors in series share the supply voltage in proportion to their values. Take the output from the middle:

Vout = Vin × R2 ÷ (R1 + R2)

Worked example12 V with R1 = 10 kΩ and R2 = 4.7 kΩ: Vout = 12 × 4.7 ÷ 14.7 = 3.84 V.

A divider only holds its voltage if whatever you connect draws much less current than the divider itself. That makes dividers good for sensing (an ADC input), and poor for powering anything.

▶LED resistorsSetting an LED's current safely

An LED drops a roughly fixed forward voltage (about 2 V for red, 3 V for blue or white). The resistor takes the rest of the supply and sets the current:

R = (Vsupply − Vforward) ÷ I

Worked exampleRed LED on 5 V at 20 mA: R = (5 − 2) ÷ 0.02 = 150 Ω. 150 Ω is a standard value, so use it.

Without a resistor, the LED's current is limited only by the supply, and it burns out in moments.

ΣKirchhoff's current lawWhat flows into a junction flows out

At any junction (node), the total current flowing in equals the total flowing out. Charge can't pile up in a wire.

ΣI in = ΣI out

Worked example3 A and 2 A flow into a node. Whatever leaves must total 5 A: if one branch carries 1.5 A, the other carries 3.5 A.

↻Kirchhoff's voltage lawAround any loop, the voltages balance

Go all the way round a closed loop and add up every rise and drop: the total is zero. The energy the source gives is all used by the loads.

ΣV = 0 around any closed loop

Worked exampleA 9 V battery feeds an LED that drops 2 V. The resistor in the same loop must drop 9 − 2 = 7 V.

◇The Wheatstone bridgeMeasuring an unknown resistance precisely

Four resistors in a diamond with a sensitive meter across the middle. When the meter reads zero, the bridge is balanced and the two ratios match:

R1 ÷ R2 = R3 ÷ R4 → R4 = R2 × R3 ÷ R1

Because it compares ratios instead of measuring current directly, a bridge is very precise. Strain gauges and many temperature sensors use one.

⌁Measuring safely with a multimeterVolts across, amps in line, ohms with the power off

Volts: put the probes across the part (in parallel). The meter has a very high resistance, so it barely disturbs the circuit.
Amps: break the circuit and put the meter in line (in series). Its resistance is tiny, so never put it across a supply in amps mode: that is a short circuit through the meter's fuse.
Ohms: the meter supplies its own small current, so the circuit must be off. With power on, the reading is wrong and the meter can be damaged.

CCConstant voltage and current limitHow a bench supply protects your circuit

A bench supply has two knobs. In CV (constant voltage) mode it holds the voltage you set and the load decides the current. If the load tries to draw more than the current limit, the supply switches to CC (constant current) and lowers its voltage until the current equals the limit.

Worked exampleSet 12 V with a 50 mA limit, then connect 100 Ω. Ohm's law wants 120 mA, so the supply goes into CC and gives 50 mA × 100 Ω = 5 V.

Setting a sensible limit before switching on is the easiest way to avoid burning parts.

Circuit calculators

The everyday sums for building circuits. Results update as you type.

Voltage divider

Vout = Vin × R2 ÷ (R1 + R2)

Vin V

R1 top, Ω

R2 bottom, Ω

LED resistor

R = (Vsupply − Vforward) ÷ I

Supply V

LED colour

Current mA

Series and parallel

Wheatstone bridge

Balanced when R1 ÷ R2 = R3 ÷ R4, so R4 = R2 × R3 ÷ R1

R1 Ω

R2 Ω

R3 Ω

KVL loop solver

Enter the voltages round a loop: sources positive, drops negative. Leave one blank to find it.

Resistor power check

P = V² ÷ R, then pick a rating at least twice that

Voltage across it V

Resistance Ω

Resistor boxes accept suffixes: 4.7k, 2k2, 1M, 470R.

Resistor colour code

Read the bands from the end they're bunched towards. The tolerance band, usually gold or brown, sits on its own at the other end.

Find the bands for a value

Everyday numbers

Typical values for things you'll meet. The resistance column is Ohm's law applied to the other two: R = V ÷ I.

Thing	Voltage	Current	Power	Works out as	Worth knowing
Red LED (with its resistor on 5 V)	2.0 V	20 mA	40 mW	100 Ω	The LED alone behaves like 100 Ω at this current, but its resistance changes with current.
Torch bulb on two AA cells	3 V	0.3 A	0.9 W	10 Ω	A cold filament has much lower resistance, so bulbs draw a surge at switch-on.
USB 2.0 port	5 V	0.5 A max	2.5 W	10 Ω min load	USB-C can negotiate 9 V, 15 V or 20 V for faster charging.
Phone fast charge (USB-C PD)	9 V	2 A	18 W	4.5 Ω	Higher voltage moves the same power with less current and less cable heating.
Car headlight bulb (H4)	12 V	4.6 A	55 W	2.6 Ω	At 12 V, power quickly means large currents and thick cables.
Car starter motor	12 V	150–300 A	2–3 kW	≈ 0.05 Ω	Why battery leads are as thick as a finger.
Kettle (Ireland, UK)	230 V	13 A	3 kW	17.7 Ω	Right at the 13 A plug fuse limit, which is why kettles are often the biggest load in a kitchen.
9 W LED lamp	230 V	39 mA	9 W	≈ 5.9 kΩ	Gives about the light of a 60 W filament bulb.
Human body, hand to hand	230 V	up to 230 mA	—	≈ 1 kΩ (wet)	About 30 mA across the chest can stop a heart. An RCD trips at 30 mA for exactly this reason.

Check yourself

Six questions. Each answer comes with the working.

Formula sheet

Everything on this page on one card.

V = I × RVoltage from current and resistance

I = V ÷ RCurrent from voltage and resistance

R = V ÷ IResistance from voltage and current

P = V × IPower from voltage and current

P = I² × RPower when you know the current

P = V² ÷ RPower when you know the voltage

R = R1 + R2 + …Resistors in series

1/R = 1/R1 + 1/R2 + …Resistors in parallel

Vout = Vin·R2/(R1+R2)Voltage divider

R = (Vs − Vf) ÷ ILED series resistor

ΣI in = ΣI outKirchhoff's current law

ΣV = 0Kirchhoff's voltage law, round any loop