Theory — Quantities and Calculations

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Units and the core electrical quantities — the foundations for every calculation. Work through each part, try the examples, then test yourself at the end.

📐 The 5 steps for any calculation

  1. Find the formula — it's on your sheet.
  2. Fix the units — change any prefixes (see the number helper).
  3. Put the numbers in.
  4. Work it out — one line at a time.
  5. Write the answer — with its unit.
Concept 1

Units, scientific notation & prefixes

Key words

Unit
what you measured (for example volt or ohm).
Prefix
a letter in front of a unit that makes it bigger or smaller (k = ×1000).
Base unit
the plain unit with no prefix (for example Ω, A, V).

Every measurement has a unit. The unit tells you what you measured (for example volts or ohms).

Big or small numbers use a prefix — a letter in front of the unit (like k for kilo). You can also write them in scientific notation, a short way to write very big or very small numbers (for example 4 700 Ω = 4.7 × 10³ Ω).

  • Current I — ampere (A) · Voltage / p.d. V — volt (V)
  • Resistance R — ohm (Ω) · Power P — watt (W)
  • Time t — second (s) · Capacitance C — farad (F) · Frequency f — hertz (Hz)
ppico · ×10⁻¹²
nnano · ×10⁻⁹
µmicro · ×10⁻⁶
mmilli · ×10⁻³
kkilo · ×10³
Mmega · ×10⁶
k base unit m µ n p
Going right (k → base → m → µ…): × 1000 each step. Going left (back the other way): ÷ 1000 each step. So 4.7 kΩ × 1000 = 4700 Ω, and 2.0 mA ÷ 1000 = 0.0020 A.

A prefix is a letter in front of a unit. k (kilo) means , while m (milli) means . The plain unit with no prefix is called the .

Practice 1

Write each value in its base unit (no prefix): (a) 4.7 kΩ   (b) 22 µF   (c) 3.3 mA   (d) 470 nF.

Answer
(a) 4.7 kΩ = 4.7 × 1000 = 4700 Ω (b) 22 µF = 22 × 10⁻⁶ = 0.000022 F (c) 3.3 mA = 3.3 ÷ 1000 = 0.0033 A (d) 470 nF = 470 × 10⁻⁹ = 0.00000047 F

✅ You can now…

  • name the unit for current, voltage, resistance and power.
  • change a value between a prefix and its base unit (× or ÷ 1000).
Concept 2

Current, voltage, resistance & power

Key words

Voltage (p.d.)
the push that moves the current. In volts (V).
Current
how much electricity flows. In amps (A).
Resistance
how hard it is for current to flow. In ohms (Ω).
Power
how fast energy is used (heat or light). In watts (W).
Ohm's law
V = I R
p.d. = current × resistance
Power
P = I V
power = current × p.d.
Power (from current)
P = I2 R
power = current² × resistance
Power (from p.d.)
P = V2R
power = p.d.² ÷ resistance
V = I R triangle VIR
Cover the one you want
P = I V triangle PIV
Cover the one you want
  • Look at what the question gives you. Pick the power formula that uses those two things.
  • A resistor turns electrical energy into heat — it gives out power.
  • Always change prefixes to the base unit before you put numbers in (use the number helper).

Voltage is the that moves the current, measured in . Resistance is how hard it is for current to flow, measured in , and power is how fast energy is used, measured in .

Substitute & solve A 4.7 kΩ resistor carries a current of 2.0 mA. Calculate the p.d. across it.
Convert first
R = 4.7 × 1000 = 4700 Ω kΩ → Ω
I = 2.0 ÷ 1000 = 0.0020 A mA → A
V=I R
V=0.0020 × 4700numbers in
V=9.4 V
Rearrange — numbers in first A resistor gives out 0.50 W of heat when 5.0 V is across it. Calculate its resistance.
P=V2R
0.50=5.02Rnumbers in first
R=5.02 ÷ 0.50now rearrange
R=25 ÷ 0.50square first
R=50 Ω
We do — fill the gaps A 2.0 kΩ resistor carries a current of 3.0 mA. Find the p.d. across it.
1 Fix the units: R = 2.0 × 1000 = Ω  ·  I = 3.0 ÷ 1000 = A
2 Formula: V = I R
3 Numbers in: V = ×
4 Answer: V = V

See the full answer
R = 2.0 × 1000 = 2000 Ω I = 3.0 ÷ 1000 = 0.0030 A V = I R = 0.0030 × 2000 V = 6.0 V
Practice 2

A 12 V supply drives a current of 0.25 A through a lamp. Calculate (a) the resistance of the lamp and (b) the power it dissipates.

Answer
(a) V = I R → R = V ÷ I = 12 ÷ 0.25 = 48 Ω (b) P = I V = 0.25 × 12 = 3.0 W

✅ You can now…

  • use V = I R for a component or a whole circuit.
  • pick and use the right power formula (P = IV, I²R or V²/R).
Interactive

Number Cruncher challenge

Ten quick questions mixing prefixes & conversions with Ohm's law and power. Type each answer in the unit shown. Score 8 / 10 to earn the 🧮 Number Cruncher badge — tap New set for fresh numbers any time.

Your questions scored

Round sensibly; answers within 1% are accepted. Decimals are fine (e.g. 0.25).

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Check

Check your understanding

Answer the multiple-choice questions, then mark yourself with the RAG self-check.

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