Electrical Principles
Ohm's Law links voltage, current and resistance. Electrical power tells engineers how much energy a device uses every second — the numbers behind every motor rating, fuse selection and cable sizing decision.
2Topics
8Examples
4Calculators
12Practice Qs
⚡Voltage, Current & ResistanceOhm's Law
💡Electrical PowerWatts and efficiency
⚙️Applications4 workshop calculators
🎮Game12 randomised questions
📝Practice12 graded questions
Why this matters in engineeringReal world
Electricians size fuses from the maximum current a cable can carry. Motor nameplates quote power in watts or kilowatts — found by multiplying voltage by current. Ohm's Law lets maintenance engineers fault-find: if the voltage is normal but the current is too high, resistance has dropped somewhere in the circuit.
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Voltage, Current & Resistance
Ohm's Law: the three quantities that describe every electrical circuit, and how to find any one of them from the other two.
⚡Ohm's Law CalculatorChoose what you want to find, enter the other two values
Choose what to find, enter the other two values, then press Calculate.
📚 Key vocabulary
- Voltage (V)
- the electrical pressure that drives current round a circuit, measured in volts.
- Current (I)
- the flow of electrons through a conductor, measured in amperes (amps).
- Resistance (R)
- opposition to the flow of current, measured in ohms (Ω).
- Ohm's Law
- the relationship V = I × R, holding for most metals at constant temperature.
- Conductor
- a material with low resistance through which current flows easily (e.g. copper).
- Insulator
- a material with very high resistance that blocks current flow (e.g. PVC cable sheath).
👁️ Visual aid — Ohm's Law circuit: current flows from battery, slows through resistance, voltage labelled
✍️Worked example 1 — finding voltage
QuestionA resistor carries a current of 3 A and has a resistance of 8 Ω. Find the voltage across it.
Formula
V = I × RSubstitute
V = 3 × 8Multiply
3 × 8 = 24AnswerV = 24 V
✍️Worked example 2 — finding current
QuestionA 230 V supply is connected to a heater element of resistance 46 Ω. Calculate the current.
Formula
I = V ÷ RSubstitute
I = 230 ÷ 46Divide
230 ÷ 46 = 5AnswerI = 5 A
✍️Worked example 3 — finding resistance
QuestionA current of 0.5 A flows when 12 V is applied to a component. What is its resistance?
Formula
R = V ÷ ISubstitute
R = 12 ÷ 0.5Divide
12 ÷ 0.5 = 24AnswerR = 24 Ω
✍️Worked example 4 — workshop cable fault
QuestionA faulty cable measures 0.8 A when connected to 24 V. A good cable carries 2.4 A at the same voltage. Calculate both resistances and explain which has the fault.
Faulty
R = 24 ÷ 0.8 = 30 ΩGood
R = 24 ÷ 2.4 = 10 ΩAnswerThe faulty cable has R = 30 Ω versus 10 Ω for the good one. The higher resistance reduces current — a sign of a loose connection or damaged conductor.
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Electrical Power
How much energy an electrical device transfers every second — and how Ohm's Law combines with power to give two more useful formulas.
💡Electrical Power CalculatorChoose a mode, enter values, press Calculate
Enter your values above and press Calculate to see every working step.
📚 Key vocabulary
- Power (P)
- the rate at which electrical energy is converted to other forms, measured in watts.
- Watt (W)
- one joule of energy transferred per second. 1 kW = 1000 W.
- Kilowatt-hour (kWh)
- the energy used by a 1 kW device running for one hour — the unit on electricity bills.
- I²R loss
- heat generated in a conductor by current; why cables must be sized for the expected current.
- Nameplate rating
- the rated power on a motor or appliance — the power at normal operating conditions.
- Fuse rating
- the maximum current a fuse will carry before melting to protect the circuit.
👁️ Visual aid — P = V × I: 230 V mains supply drives 5 A through a heater, 1150 W dissipated as heat
✍️Worked example 5 — power of a heater
QuestionA workshop heater operates at 230 V and draws a current of 5 A. Calculate its power.
Formula
P = V × ISubstitute
P = 230 × 5Multiply
230 × 5 = 1150AnswerP = 1150 W (= 1.15 kW)
✍️Worked example 6 — power using I²R
QuestionA current of 4 A flows through a cable with resistance 2.5 Ω. Calculate the power lost as heat.
Formula
P = I² × RSquare first
I² = 4 × 4 = 16Substitute
P = 16 × 2.5Multiply
16 × 2.5 = 40AnswerP = 40 W lost as heat in the cable
✍️Worked example 7 — finding current from power and voltage
QuestionA 2.3 kW motor runs at 230 V. What current does it draw?
Convert
2.3 kW = 2300 WRearrange
I = P ÷ V = 2300 ÷ 230Divide
2300 ÷ 230 = 10AnswerI = 10 A
✍️Worked example 8 — energy used
QuestionA 3 kW workshop heater runs for 2.5 hours. How much energy does it use, in kWh?
Formula
E = P × tSubstitute
E = 3 × 2.5Multiply
3 × 2.5 = 7.5AnswerE = 7.5 kWh
⚙️
Engineering Applications
Four practical electrical calculators for workshop and manufacturing tasks.
⚡ Fuse selection — maximum current
Choose the correct fuse by calculating the current an appliance draws at its rated power and supply voltage.
I = P ÷ V
🧮 Calculator
Enter power and voltage, then press Calculate.
💡 Motor nameplate — power rating
Read the running current and supply voltage from a motor nameplate to confirm its power rating.
P = V × I
🧮 Calculator
Enter voltage and current, then press Calculate.
🔥 Cable heat loss — I²R
Calculate the heat wasted in a cable run — used in cable sizing to avoid overheating.
P = I² × R
🧮 Calculator
Enter current and cable resistance, then press Calculate.
🔌 Sensor circuit — Ohm's Law check
Verify a sensor or transducer is within specification: measure the voltage and current, calculate the resistance.
R = V ÷ I
🧮 Calculator
Enter voltage and current, then press Calculate.
🎮
Electrical Challenge
12 randomised questions per round. New numbers every time.
⚡ Quick-fire round
Question 1 / 12
Score: 0
Streak: 0 🔥
Press Start to begin!
📝
Practice Questions
12 graded questions. Attempt each on paper first, then reveal the full worked solution.
Use V = I × R and P = V × I throughout. Show the formula, the substitution and every step.
Question 1 · Ohm's Law1 mark
A resistor carries 2 A when 10 V is applied. Find its resistance.
R = V ÷ I = 10 ÷ 2 = 5 Ω
Question 2 · Ohm's Law2 marks
A 24 V supply is connected to a solenoid with resistance 8 Ω. Calculate the current.
I = V ÷ R
I = 24 ÷ 8 = 3 A
I = 24 ÷ 8 = 3 A
Question 3 · Ohm's Law2 marks
A current of 0.4 A flows through a component with resistance 50 Ω. Find the voltage.
V = I × R
V = 0.4 × 50 = 20 V
V = 0.4 × 50 = 20 V
Question 4 · Ohm's Law2 marks
A PLC sensor output measures 5 V and passes 0.025 A. Calculate its resistance.
R = V ÷ I
R = 5 ÷ 0.025 = 200 Ω
R = 5 ÷ 0.025 = 200 Ω
Question 5 · Power1 mark
A lamp operates at 12 V and draws 0.5 A. What is its power?
P = V × I = 12 × 0.5 = 6 W
Question 6 · Power2 marks
A 230 V mains heater draws 8 A. Calculate its power in kW.
P = V × I
P = 230 × 8 = 1840 W
1840 ÷ 1000 = 1.84 kW
P = 230 × 8 = 1840 W
1840 ÷ 1000 = 1.84 kW
Question 7 · Power2 marks
A 3.68 kW motor runs at 230 V. What current does it draw?
3.68 kW = 3680 W
I = P ÷ V = 3680 ÷ 230 = 16 A
I = P ÷ V = 3680 ÷ 230 = 16 A
Question 8 · I²R2 marks
A cable carries 6 A and has a resistance of 1.5 Ω. Calculate the power lost as heat.
P = I² × R
I² = 6 × 6 = 36
P = 36 × 1.5 = 54 W
I² = 6 × 6 = 36
P = 36 × 1.5 = 54 W
Question 9 · Energy2 marks
A 2 kW press brake runs for 3.5 hours. How much energy does it use in kWh?
E = P × t = 2 × 3.5 = 7 kWh
Question 10 · Ohm's Law2 marks
Two cables in series have resistances of 3 Ω and 7 Ω (total = 10 Ω). If 50 V is applied, find the current.
I = V ÷ R
I = 50 ÷ 10 = 5 A
I = 50 ÷ 10 = 5 A
Question 11 · Combined3 marks
A 400 V motor draws 12 A. Calculate (a) the power in kW, and (b) the energy used in 4 hours in kWh.
P = V × I = 400 × 12 = 4800 W = 4.8 kW
E = P × t = 4.8 × 4 = 19.2 kWh
E = P × t = 4.8 × 4 = 19.2 kWh
Question 12 · Combined3 marks
A cable of resistance 0.8 Ω carries a current that produces 72 W of heat loss. Find the current, then calculate the voltage drop across the cable.
P = I² × R → I² = P ÷ R = 72 ÷ 0.8 = 90
I = √90 ≈ 9.49 A
V = I × R = 9.49 × 0.8 ≈ 7.6 V
I = √90 ≈ 9.49 A
V = I × R = 9.49 × 0.8 ≈ 7.6 V