Electricity Calculator V = IR
Calculate voltage, current, resistance, power, and energy with step-by-step solutions. Perfect for GCSE and A-Level Physics.
Voltage = Current × Resistance
Solve for:
Quick Examples
Ohm's Law
GCSEVoltage = Current × Resistance
Power (basic)
GCSEPower = Current × Voltage
Power (from R)
A-LevelPower from current and resistance
Power (from V)
A-LevelPower from voltage and resistance
Energy
GCSEEnergy = Power × Time
Energy (from charge)
A-LevelEnergy = Charge × Voltage
What is Ohm's Law?
Ohm's Law is one of the most fundamental equations in electronics and physics. Discovered by Georg Ohm in 1827, it describes the relationship between voltage, current, and resistance in an electrical circuit.
The V-I-R Triangle
Voltage (V) = Current (A) × Resistance (Ω)
Find current
Find voltage
Find resistance
The units are: Volts (V) for voltage, Amps (A) for current, and Ohms (Ω) for resistance. One Ohm is the resistance that allows one Amp to flow when one Volt is applied.
Example: A 12V battery connected to a 4Ω resistor
I = V/R = 12/4 = 3 A
Electrical Power
Electrical power is the rate at which electrical energy is transferred by an electric circuit. The unit of power is the Watt (W).
P = IV
Power = Current × Voltage
Basic formula
P = I²R
Power = Current² × Resistance
When you know I and R
P = V²/R
Power = Voltage² / Resistance
When you know V and R
Common Appliance Power Ratings
Series vs Parallel Circuits
Understanding the difference between series and parallel circuits is crucial for GCSE and A-Level Physics exams.
Series Circuits
- • Current is the same through all components
- • Voltages add up: V_total = V₁ + V₂ + ...
- • Resistances add up
- • One component fails = whole circuit fails
Parallel Circuits
- • Voltage is the same across all branches
- • Currents add up: I_total = I₁ + I₂ + ...
- • Reciprocals add up
- • One component fails = others still work
⚠️ Common mistake: Students often add resistances in parallel like series. Remember: in parallel, use the reciprocal formula. The total resistance is always less than the smallest individual resistance.
Electrical Energy & Cost
Electrical energy is measured in Joules (J), but electricity bills use kilowatt-hours (kWh).
Energy Formula
E = PtEnergy = Power × Time
Cost Formula
Cost = kWh × priceUK average: ~£0.30 per kWh
Converting Units
1 kWh = 1,000 W × 1 hour = 1,000 W × 3,600 s = 3,600,000 J
Example: 2kW kettle for 30 mins = 2 × 0.5 = 1 kWh = ~£0.30
Common Mistakes in Electricity Problems
Avoid these frequent errors when solving electricity questions in GCSE and A-Level Physics exams:
Confusing series and parallel formulas
Series: add resistances directly. Parallel: add reciprocals (1/R). Mixing these up gives completely wrong answers.
Ask: 'Is current the same (series) or voltage the same (parallel)?'
Forgetting to convert mA to A
Ohm's Law needs current in Amps, not milliamps. 500 mA = 0.5 A. Using 500 instead of 0.5 gives an answer 1000× wrong.
Always convert: divide milliamps by 1000 to get Amps.
Using wrong power formula
There are three power formulas (P=IV, P=I²R, P=V²/R). Using the wrong one when you have different known values leads to errors.
Choose the formula that uses the values you actually know.
Not converting time to seconds for energy
E = Pt gives Joules only when P is in Watts and t is in seconds. Using minutes or hours without conversion gives wrong units.
For Joules: use seconds. For kWh: use hours and kW.
Adding resistances in parallel
In parallel, 10Ω + 10Ω ≠ 20Ω. The reciprocal rule gives 1/10 + 1/10 = 2/10, so R = 5Ω.
Parallel total is always LESS than the smallest resistor.
Mixing up V, I, and R positions
In V = IR, voltage is on one side alone. Students often write I = VR or R = VI, which are wrong rearrangements.
Use the V-I-R triangle: V on top, I and R on bottom.
Worked Examples
Practice with these GCSE and A-Level style electricity problems:
Example 1: Finding Current
A 12V battery is connected to a 4Ω resistor. Calculate the current flowing.
Solution:
Given: V = 12V, R = 4Ω, I = ?
Formula: I = V/R
I = 12/4
I = 3 A
Example 2: Kettle Power
A kettle draws 8.7A from the 230V mains. Calculate its power rating.
Solution:
Given: I = 8.7A, V = 230V, P = ?
Formula: P = IV
P = 8.7 × 230
P = 2001 W ≈ 2 kW
Example 3: Parallel Resistors
Two resistors of 6Ω and 12Ω are connected in parallel. Find the total resistance.
Solution:
Formula: 1/R_total = 1/R₁ + 1/R₂
1/R_total = 1/6 + 1/12
1/R_total = 2/12 + 1/12 = 3/12 = 1/4
R_total = 4 Ω
(Note: less than the smallest resistor, as expected for parallel)
Example 4: Electricity Cost
A 2kW heater runs for 3 hours. How many kWh of energy does it use and what does it cost at £0.30/kWh?
Solution:
Energy = Power (kW) × Time (hours)
Energy = 2 kW × 3 h = 6 kWh
Cost = 6 kWh × £0.30
Cost = £1.80
Frequently Asked Questions
What is Ohm's Law?
V = IR states that voltage equals current times resistance. It's the foundation of circuit analysis.
How do I calculate resistance?
Use R = V/I. Divide voltage (Volts) by current (Amps) to get resistance in Ohms (Ω).
What is the difference between voltage and current?
Voltage is the 'push' (potential difference) measured in Volts. Current is the flow rate of charge, measured in Amps.
How do I calculate power?
Use P = IV, P = I²R, or P = V²/R depending on what values you know. Power is in Watts.
Series or parallel: which has more resistance?
Series has more (resistances add). Parallel has less (always less than the smallest resistor).
What is a kilowatt-hour?
1 kWh = using 1kW for 1 hour = 3,600,000 J. It's the unit on electricity bills.
Why does P = I²R cause heating?
High current through high resistance generates lots of heat. The I² means doubling current quadruples heat.
Is this calculator suitable for exams?
Yes! It covers all GCSE and A-Level electricity topics with step-by-step solutions.
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