Charge, Current, and Voltage

Charge as Flow

current is charge per second

Current is how much charge flows past each second. Multiply current by time and you get the total charge that went by.

Example

Current is how much charge flows past each second. Multiply current by time and you get the total charge that went by. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Current is charge per second

Current is the amount of charge that flows past a point each second, measured in amperes. In this wire the current is 3 amperes, so 3 coulombs of charge pass the marked point every second.

I=3 A(ampere=coulomb per second)I = 3\ \text{A} \quad (\text{ampere} = \text{coulomb per second})
Charge flows along a wireA straight wire with an arrow marking the direction and size of the current through it.3 Acharge flows

Charge is current multiplied by time

If that current runs for a time, the total charge that flows past is the current times the time. The ampere-times-second leaves a coulomb, which is a unit of charge.

Q=I⋅tQ = I \cdot t

A fixed time turns current into charge

Hold the time at 4 seconds. A larger current passes more charge in that same time, so the charge column grows in equal steps.

ItQ1 A4 s4 C2 A4 s8 C3 A4 s12 C\begin{array}{c|c|c}I & t & Q \\1\ \text{A} & 4\ \text{s} & 4\ \text{C} \\2\ \text{A} & 4\ \text{s} & 8\ \text{C} \\3\ \text{A} & 4\ \text{s} & 12\ \text{C}\end{array}
Charge flows along a wireA straight wire with an arrow marking the direction and size of the current through it.3 Acharge flows

A fixed current keeps adding charge

Now hold the current at 3 amperes and let the clock run longer. The same flow rate keeps adding another chunk of charge each time, so doubling the time doubles the charge that has passed.

ItQ3 A2 s6 C3 A4 s12 C3 A6 s18 C\begin{array}{c|c|c}I & t & Q \\3\ \text{A} & 2\ \text{s} & 6\ \text{C} \\3\ \text{A} & 4\ \text{s} & 12\ \text{C} \\3\ \text{A} & 6\ \text{s} & 18\ \text{C}\end{array}
Charge flows along a wireA straight wire with an arrow marking the direction and size of the current through it.3 Acharge passed

Substitute the current and the time

Put in the current of 3 amperes and a time of 4 seconds.

Q=3 A ⋅ 4 sQ = 3\ \text{A} \,\cdot\, 4\ \text{s}

Compute the charge

Multiplying gives 12 coulombs of charge passed through. Current tells you the rate; multiply by the time to get how much charge went by.

Q=12 CQ = \hl{12}\ \text{C}
Charge flows along a wireA straight wire with an arrow marking the direction and size of the current through it.3 Acharge passed
electricity Clean numbers throughout: a current of 3 A running for 4 s moves exactly 12 C of charge, so the ampere really is a coulomb per second.