Current ElectricityElectric Current
Imagine a small window, an imaginary flat area, held across the flow of charges. Positive and negative charges may cross it in both directions, forward and backward. In a time , let be the net amount (forward minus backward) of positive charge that crosses the window in the forward direction, and the net amount of negative charge that crosses it forward.
Here the positive charges move forward through the window, while the electrons move backward. The net charge that crosses in the forward direction is
and the current across the window, in the forward direction, is
If comes out negative, the current is in the backward direction. In 2 s, suppose 4 C of positive charge crosses forward and 6 C of negative charge crosses backward. Negative charge going backward means
So negative charge moving backward adds to the current forward, exactly as much as positive charge moving forward would. That is why, in a metal wire where only electrons move, the current points opposite to the way the electrons travel.
Current at an Instant
works only when the current is steady, so that the charge grows in proportion to the time. Aman plugs his phone into a fast charger, and for the first few seconds the charger ramps its current up. The total charge that has entered the phone after seconds is coulomb, the blue curve below. What is the current at the instant s, the point P?
Take a short interval after P. The amber chord has slope : the average current over that interval. Shrink it: Δt =
As shrinks, the chord turns into the tangent at P and settles on one value: the current at s is
the slope of the charge–time graph. For a steady current the graph is a straight line, and every interval gives the same answer, .
The SI unit of current is the ampere (A). It is defined through the magnetic effects of currents, which you will meet in the next chapter. One ampere is a flow of one coulomb per second.
From Nerves to Lightning
An ampere is roughly the current in a household appliance. Currents in nature and in machines range over a staggering span. Arrange these from the smallest current to the largest.
Nerve signals carry currents of microamperes ( A), a torch bulb a few tenths of an ampere, a room heater about ten amperes, and an average lightning stroke tens of thousands of amperes.
Speed Round: Charge and Current
, , and the number of electrons with C. Minutes become seconds first.
Get five right to move on.