Library / Electrical / ELE-01
Electrical
Electric charge
Charge moved by a steady current in a given time.
- Ref
- ELE-01
- Rev
- v1
- Field
- Electrical
- Result
- Q [C]
Q in coulombs (C), I in amperes (A), t in seconds (s). For a varying current, Q is the area under the current–time graph.
Current is the rate at which charge flows, so the charge that passes is the current multiplied by the time it flows for. One ampere flowing for one second moves one coulomb.
Calculator
- Charge in mAh16.67 mAh
- Electrons transferred3.745×1020
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Charge is the product of current and time, so doubling either one doubles Q. The sweep chart over either variable is a straight line.
- Battery capacity is quoted in ampere-hours: 1 Ah = 3600 C, so 1 mAh = 3.6 C.
- One coulomb is about 6.24×1018 electrons, so ordinary currents move enormous numbers of charge carriers.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (C) | Local step | Change in result |
|---|---|---|---|---|---|---|
| t Time | 1 to 3,600 s | 2 | 7,200 | 7,198 | +10% | +10 % |
| I Current | 0.1 to 20 A | 3 | 600 | 597 | +10% | +10 % |
Sweep of Time
| Time (s) | Charge (C) |
|---|---|
| 1 | 2 |
| 2.783 | 5.566 |
| 7.746 | 15.49 |
| 21.56 | 43.12 |
| 60 | 120 |
| 167 | 334 |
| 464.8 | 929.5 |
| 1,293 | 2,587 |
| 3,600 | 7,200 |
Sweep one variable
Variables and how each one contributes
Charge
What the equation gives you. Everything else feeds it.
Current
Steady rate of flow of charge past a point. Directly proportional: doubling the current doubles the charge moved in the same time.
Time
How long the current flows. Directly proportional: charge builds up in step with time.
Worked example with the values above
- Check the units: ampere × second = coulomb.
- Q = It = 2 A × 30 s = 60 C.
- In battery terms, 60 C is 16.67 mAh (1 mAh = 3.6 C).
Assumptions and limits
- Steady (constant) current for the whole time.
- For a varying current use Q = ∫I dt, the area under the I–t graph.
- Conventional current: the charge carriers may be electrons moving the other way.
Common mistakes
- Mixing time units: t must be in seconds for Q in coulombs (3600 s per hour).
- Confusing charge Q (coulombs) with current I (amperes).
- Reading mAh as a unit of energy. It is a unit of charge. Energy also needs the voltage (Wh = Ah × V).
Statistics and uncertainty
The formula is deterministic. When I and t are measured, the uncertainty in Q follows from theirs: for independent errors, δQ/Q ≈ √[(δI/I)² + (δt/t)²]. If the current varies during the interval, use the average current or integrate I over time.
Where it is used
- Battery capacity and runtime estimates.
- Charge delivered by a pulse, for sizing a capacitor or battery for a pulsed load.
- First step before finding electrical work, W = QV.
Maths you need
- Units and prefixes: mAh, mA and s: convert to SI before substituting
- Rates: current is charge per unit time, I = Q / t