Quantity of electricity
Q = I · t
| Quantity | Symbol | Unit |
|---|---|---|
| Quantity of electricity | Q | C |
| Current | I | A |
| Time | t | s |
Elec Class
learn electricity hands-on
Lesson · chapter 3 of 15
Voltage (in volts) is the potential difference between two points, which pushes the charges; current (in amps) is the amount of charge flowing through a wire each second: I = Q / t. For a current to flow, you need a voltage and a closed circuit.
The result is worked out before your eyes, line by line, just like on the board.
1I'm looking for
2I enter the known values
Formula used Q = I · t
3The result
Electric charge Q7,200 C
A current of 2 A flowing for 3,600 s carries 7,200 C.
The definition, the key points to remember and everyday examples.
The voltage U between two points is the difference of their potentials (V_A − V_B), in volts: it sets the charges in motion. The current I is the flow of charge, in amperes: 1 A = 1 C/s. By convention it flows from + to − outside the generator (electrons go the other way).
The quantity of electricity Q = I·t is counted in coulombs or ampere-hours. The current density J = I/S (A/mm²) limits the heating of a conductor. The European mains delivers 230 V phase to neutral, 400 V between phases.
Voltage is the difference in height between the water tower and your tap: the bigger it is, the harder the water pushes. Current is the flow rate, in liters per second, just as current counts coulombs per second. With the tap closed, the pressure is there but nothing flows: that's an open circuit, with voltage and no current. Where it falls short: in a wire, the charges are already everywhere and don't drain away like a tank.
| Quantity | Symbol | Unit |
|---|---|---|
| Quantity of electricity | Q | C |
| Current | I | A |
| Time | t | s |
| Quantity | Symbol | Unit |
|---|---|---|
| Current density | J | A/mm² |
| Current | I | A |
| Cross-section | S | mm² |
| Quantity | Symbol | Unit |
|---|---|---|
| Cross-section | S | mm² |
| Diameter | d | mm |
Four steps to solve a problem, then an example solved line by line.
A voltage between two points, a current in a branch, an electric charge or a current density?
Hours to seconds (× 3,600) for coulombs, keep hours for amp-hours; cross-section in mm² for J in A/mm².
Q = I × t, I = Q / t or t = Q / I; for a round wire, first calculate S = π × d² / 4, then J = I / S.
A battery lasts hours, not seconds; a household wire carries a few amps per mm², not hundreds.
A 40 Ah battery delivers a steady current of 2 A. How long can it last? What quantity of electricity, in coulombs, does that represent? A 1.5 mm² wire carrying 10 A: what current density?
Q = I · t so t = Q / I = 40 / 2 = 20 h.
In coulombs: 40 Ah × 3 600 = 144 000 C (1 Ah = 3 600 C).
J = I / S = 10 / 1.5 = 6.7 A/mm²: too much for a domestic installation (5 to 6 A/mm² is accepted), the wire would heat up.
From the charge and the time: I = Q / t. For example, 600 C in 5 minutes (300 s) gives I = 600 / 300 = 2 A. In a circuit, you can also find it with Ohm's law, I = U / R.
The voltmeter is connected in parallel, across both terminals of the component; the ammeter in series, in the opened circuit, so that the current flows through it. An ammeter connected in parallel creates a short circuit and often blows its fuse.
Because of a convention set in the 19th century, before the electron was discovered (1897). The chosen direction turned out to be opposite to the electrons' motion, but all calculations remain correct: the convention was kept.
It's the current flowing through the body that causes injury: a few tens of milliamps are enough, hence the 30 mA threshold of residual current devices. But it's the voltage that drives this current: above 50 V AC, it is considered dangerous.
Current is the phenomenon, charges moving; its intensity is its measurement, in amps. In everyday use, "a current of 2 A" simply means a current whose intensity is 2 A.
Both their feet touch the same wire, at the same potential: the voltage between them is almost zero, so no current flows through them. A bird touching two wires at once, or a wire and a pylon, would be electrocuted.
Voltage is the "pressure" that pushes the charges, in volts, between two points; current is the resulting flow of charges, in amperes, through a conductor. Without a closed circuit there is a voltage but no current.
3 600 C: one ampere for one hour, i.e. 3 600 seconds. A 40 Ah battery thus stores 144 000 C.
From the simplest to the most complete, each problem comes with a step-by-step solution.
In the lab, measure the voltage across the battery, the switch and the resistor, with the switch open then closed: students see that when open, the switch has the full battery voltage across it while no current flows.
Using Elec Class in class