Each electron that travels through a circuit carries 1.602 x 10^-19 coulombs of charge. The circuit's current measures the flow of this charge, with billions upon billions of electrons adding up to a significant charge flow. The longer a current flows, the more charge it carries. You can calculate the current through a circuit, and the result charge that passes through it, from the circuit's voltage and resistance.
Add together the resistances of the circuit's resistors. If it has, for instance, two resistors of 3 ohms and 5 ohms each: 3 + 5 = 8 ohms.
Divide the voltage across the circuit by this total resistance. With a voltage, for instance, of 12 volts: 12 / 8 = 1.5. This is the current through the circuit, measured in amperes.
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Multiply the current by the length of time for which it runs. If the current runs, for instance, for 10 seconds: 1.5 x 10 = 15. This is the number of coulombs of charge that pass through the circuit.