Current and EMF

A circuit is just a loop — wires connecting a battery to some stuff (a bulb, a motor, a resistor) and back to the battery. Plug a phone charger into the wall and you’ve completed a circuit. Flip a light switch and you’ve completed (or broken) one.

Before you can analyze any circuit on the MCAT, you need to know two basic things: what’s actually moving through the wires, and what’s pushing it. Those are current (the flow of charge) and EMF (the energy source pushing it). Get these two ideas right and the rest of circuit analysis is just bookkeeping.

What Is Electric Current?

Picture a packed school hallway between classes. No single student is sprinting — most are shuffling. But the crowd as a whole moves steadily toward the next class. Electric current works the same way. Individual electrons drift slowly through a wire — often less than a millimeter per second — but the collective movement of trillions of charges per second produces the measurable flow we call current.

Current is a scalar (just magnitude), but we still assign it a direction for circuit analysis — and that’s where the next quirk comes in.

Conventional Current vs. Electron Flow

A weird piece of physics history that the MCAT expects you to know:

When Benjamin Franklin first described electricity in the 1700s, he guessed that positive charges flowed from the + terminal to the − terminal. He guessed wrong. We now know that electrons (negatively charged) actually flow from − to +. But Franklin’s convention got baked into all the math and circuit symbols, and we never bothered to flip it.

So:

• Conventional current flows + → − through the external circuit. (This is the convention used in every formula and diagram.)
• Electron flow is the opposite: − → +.

On the MCAT, always use conventional current unless the question explicitly asks about electron flow.

The Water-Park Analogy

A complete circuit is a lot like a water park.

• Battery = the pump that lifts water to the top of the park (provides energy to the charges).
• Wires = wide pipes that carry water with very little resistance.
• Resistor = a narrow, twisting slide where water loses energy as it tumbles down (charges lose energy as they pass through).

Crucial rule: water has to return to the pump. If you break the loop (open circuit), nothing flows.

Electromotive Force (EMF)

Despite the misleading name, EMF is not actually a force. It’s a voltage — specifically, the voltage that a battery (or other energy source) provides to push charge around a circuit.

An ideal battery maintains constant EMF no matter how much current flows. Real batteries have internal resistance (covered in §6.5), which eats up some of the energy and reduces the voltage available to the rest of the circuit.

Requirements for Current to Flow

For steady current to actually exist, you need both:

1. A complete (closed) loop. Any break anywhere stops all current — not just at the break. This is exactly why a single burned-out bulb in a series string of holiday lights kills the whole strand.

2. A source of EMF. Something has to do work on the charges to keep them moving. Without a battery (or generator, or solar cell), any current would die out within microseconds as charges lose energy to resistance.

Worked Example

A wire carries a current of 0.5 A. How many coulombs of charge pass a given cross-section in 1 minute? How many electrons is that?

• Charge: $Q = It = 0.5 \times 60 = 30$ C.
• Each electron carries $1.6 \times 10^{-19}$ C, so number of electrons $= 30/(1.6 \times 10^{-19}) \approx 1.9 \times 10^{20}$ electrons.

That’s almost $10^{20}$ electrons per minute through a wire carrying just half an amp. Even a small current involves an unimaginable number of electrons.