Electricity Calculations and Exam Practice

This lesson brings together all the equations and problem-solving skills from the electricity topic — as required by the Edexcel GCSE Physics specification (1PH0). You will practise combining formulae in multi-step problems, selecting the correct equation, avoiding common mistakes, and approaching circuit analysis systematically.

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Key Equations — Complete Reference

Before tackling problems, make sure you know all the key electricity equations:

Equation	What It Calculates	Variables
I = Q / t	Current	I = current (A), Q = charge (C), t = time (s)
V = W / Q	Potential difference	V = voltage (V), W = energy (J), Q = charge (C)
V = IR	Ohm's law	V = voltage (V), I = current (A), R = resistance (Ω)
P = IV	Power	P = power (W), I = current (A), V = voltage (V)
P = I²R	Power	P = power (W), I = current (A), R = resistance (Ω)
P = V²/R	Power	P = power (W), V = voltage (V), R = resistance (Ω)
E = Pt	Energy	E = energy (J), P = power (W), t = time (s)
E = QV	Energy	E = energy (J), Q = charge (C), V = voltage (V)
Cost = E (kWh) × price	Electricity cost	E in kWh, price per kWh

Series vs Parallel at a Glance

Series	Parallel
Same current through both bulbs	Same voltage across both bulbs
Cell voltage splits across them	Current splits between branches

Both circuits use the same cell and two identical bulbs — only the wiring differs. In the series version there is a single loop, so the current that passes through Bulb 1 must also pass through Bulb 2 (no choice). In the parallel version the wire splits into two independent branches, so each bulb is connected straight across the cell terminals and sees the full cell voltage.

Series Circuit Rules

Rule	Equation
Current is the same everywhere	I₁ = I₂ = I₃
Voltages add up	V_total = V₁ + V₂ + V₃
Resistances add up	R_total = R₁ + R₂ + R₃

Parallel Circuit Rules

Rule	Equation
Voltage is the same across each branch	V₁ = V₂ = V₃
Currents add up	I_total = I₁ + I₂ + I₃
Reciprocal of resistances (Higher)	1/R_total = 1/R₁ + 1/R₂

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Choosing the Right Equation

The most important skill in electricity calculations is selecting the correct equation. Here is a systematic approach:

graph TD
    A["What are you asked<br/>to find?"] --> B{"Power?"}
    A --> C{"Current?"}
    A --> D{"Resistance?"}
    A --> E{"Energy?"}
    A --> F{"Voltage?"}
    B -- "Know I and V" --> G["P = IV"]
    B -- "Know I and R" --> H["P = I²R"]
    B -- "Know V and R" --> I["P = V²/R"]
    C -- "Know V and R" --> J["I = V/R"]
    C -- "Know Q and t" --> K["I = Q/t"]
    D -- "Know V and I" --> L["R = V/I"]
    E -- "Know P and t" --> M["E = Pt"]
    E -- "Know Q and V" --> N["E = QV"]
    F -- "Know I and R" --> O["V = IR"]
    F -- "Know W and Q" --> P["V = W/Q"]

    style A fill:#2c3e50,color:#fff
    style G fill:#27ae60,color:#fff
    style H fill:#27ae60,color:#fff
    style I fill:#27ae60,color:#fff
    style J fill:#27ae60,color:#fff
    style K fill:#27ae60,color:#fff
    style L fill:#27ae60,color:#fff
    style M fill:#27ae60,color:#fff
    style N fill:#27ae60,color:#fff
    style O fill:#27ae60,color:#fff
    style P fill:#27ae60,color:#fff

Exam Tip: Before starting any calculation, identify what you know and what you need to find. Write down the known values with units, select the equation, substitute, and solve. Always show your working — even if the final answer is wrong, you can earn method marks.

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Multi-Step Worked Examples

Example 1: Finding Current, Then Power, Then Energy

A 12 V battery is connected to a 6 Ω resistor. Calculate the energy transferred in 5 minutes.

Step 1: Find the current I = V / R = 12 / 6 = 2 A

Step 2: Find the power P = IV = 2 × 12 = 24 W

Step 3: Find the energy Convert time: 5 minutes = 5 × 60 = 300 s E = Pt = 24 × 300 = 7200 J (or 7.2 kJ)

Alternatively, in one step: E = V²t / R = (12² × 300) / 6 = (144 × 300) / 6 = 43200 / 6 = 7200 J ✔

Example 2: Series Circuit Analysis

Three resistors (2 Ω, 3 Ω and 5 Ω) are connected in series to a 10 V battery.

a) Total resistance: R_total = 2 + 3 + 5 = 10 Ω

b) Current: I = V / R = 10 / 10 = 1 A

c) Voltage across each resistor: V₁ = IR₁ = 1 × 2 = 2 V V₂ = IR₂ = 1 × 3 = 3 V V₃ = IR₃ = 1 × 5 = 5 V

d) Check: 2 + 3 + 5 = 10 V ✔ (equals the battery voltage)

e) Power dissipated by the 5 Ω resistor: P = I²R = 1² × 5 = 5 W

Example 3: Parallel Circuit Analysis

Two resistors (10 Ω and 15 Ω) are connected in parallel to a 6 V battery.

a) Current through the 10 Ω resistor: I₁ = V / R₁ = 6 / 10 = 0.6 A

b) Current through the 15 Ω resistor: I₂ = V / R₂ = 6 / 15 = 0.4 A

c) Total current from the battery: I_total = 0.6 + 0.4 = 1.0 A

d) Total resistance (Higher): 1/R_total = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 R_total = 30/5 = 6 Ω

Check: I = V/R = 6/6 = 1.0 A ✔

Example 4: Fuse Selection

A 2.5 kW kettle is connected to the 230 V mains supply. Which fuse should be used: 3 A or 13 A?

Step 1: Convert power P = 2.5 kW = 2500 W

Step 2: Calculate current I = P / V = 2500 / 230 = 10.87 A

Step 3: Choose the fuse The fuse must have a rating above 10.87 A but as close as possible. 3 A fuse: too low (would blow during normal use). 13 A fuse: above 10.87 A ✔

Answer: 13 A fuse

Example 5: Electricity Cost Calculation

A 3 kW immersion heater is used for 1.5 hours. Electricity costs 34p per kWh.

Step 1: Calculate energy E = P × t = 3 × 1.5 = 4.5 kWh

Step 2: Calculate cost Cost = 4.5 × 34 = 153p (or £1.53)

Example 6: Charge and Energy

A battery has a voltage of 9 V. A current of 0.5 A flows for 4 minutes.

a) Total charge: t = 4 × 60 = 240 s Q = It = 0.5 × 240 = 120 C

b) Energy transferred: E = QV = 120 × 9 = 1080 J

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Common Exam Mistakes

Mistake 1: Mixing Up Series and Parallel Rules

	Series	Parallel
Current	Same everywhere	Splits at junctions
Voltage	Shared (adds up)	Same across each branch
Resistance	Adds up	Less than the smallest

How to avoid: Ask yourself: "Is there only one path (series) or multiple paths (parallel)?"

Mistake 2: Forgetting Unit Conversions

Common Conversion Errors	Correct Conversion
Minutes to seconds	× 60
Hours to seconds	× 3600
kW to W	× 1000
kWh to J	× 3.6 × 10⁶

Mistake 3: Using the Wrong Power Equation

Always check which quantities you are given before choosing P = IV, P = I²R, or P = V²/R.

Mistake 4: Not Showing Working

Even if you can do the calculation in your head, always show your working. Write the equation, substitute the values, and give the answer with units. This ensures you earn method marks if you make a numerical error.

Mistake 5: Incorrect Fuse Selection