Electricity — Current, Voltage, Resistance & Power

Current, voltage, resistance, and power are the four ideas behind most beginner electricity questions. Current is charge flow, voltage is the electric potential difference that can drive that flow, resistance limits it, and power tells you how fast electrical energy is transferred. Treat them as one connected system and circuit problems stop looking like disconnected formulas.

The Formulas and Their Symbols

Current is the rate of charge flow:

Its SI unit is the ampere; one ampere means one coulomb passes a point each second.

Voltage is the electric potential difference between two points: how much electrical energy changes per unit charge. It does not flow through the wire; it is a difference between two points, which is why it is described as an electrical "push."

Resistance appears through Ohm's law, valid for a component that is approximately ohmic over the range of interest:

This works for many resistor problems but not for every device.

Power is the rate of energy transfer:

with SI unit the watt ($1\ \mathrm{W} = 1\ \mathrm{J/s}$). For an approximately ohmic resistor you can also write

Why These Forms Hold

The extra power forms are not new facts to memorize; they come straight from combining $P = VI$ with Ohm's law. Substitute $V = IR$ into $P = VI$ and you get $P = (IR)I = I^2 R$. Substitute $I = V/R$ instead and you get $P = V(V/R) = V^2/R$. That is why the ohmic condition matters: those two forms inherit it from Ohm's law.

The same connectedness explains the everyday behavior. With resistance fixed, more voltage gives more current. With voltage fixed, more resistance gives less current. Once voltage and current are known, power tells you how fast energy is delivered. So a simple resistor problem usually leans on just $V = IR$ and $P = VI$.

Worked Example: A 12 V Source and a 6 Ohm Resistor

A $6\ \Omega$ resistor is connected across a $12\ \mathrm{V}$ source, treated as ohmic.

Current first:

Then power:

Cross-check with the resistor-only form:

Both routes agree at $24\ \mathrm{W}$. A fast mental model: current is "how much charge moves each second," power is "how fast energy is delivered." A circuit can carry noticeable current with little power if the voltage is small, or large power when both voltage and current are large.

Practice and Check

Keep the $12\ \mathrm{V}$ source but change the resistor to $3\ \Omega$. Find the new current and power, then compare with the $6\ \Omega$ case.

You should get $I = 12/3 = 4\ \mathrm{A}$ and $P = (12)(4) = 48\ \mathrm{W}$. Sanity check: halving the resistance doubled the current and doubled the power, which fits $P = V^2/R$ with $V$ held fixed. As a second check, if you raised the source on the original $6\ \Omega$ resistor to $24\ \mathrm{V}$, the current would double but the power would quadruple, since $P$ scales with $V^2$.

Calculation Traps to Avoid

• Mixing up voltage and current. Voltage is a potential difference; current is charge flow.
• Using $V = IR$ on any component without checking that an ohmic model is reasonable.
• Treating power as energy. Power is a rate, not an amount.
• Dropping units, especially milliamps, kilohms, and milliwatts.
• Assuming doubling voltage doubles power. For a fixed resistor, power scales with $V^2$, not just $V$.

Where These Basics Show Up

These ideas appear in school circuit problems, household electricity, battery-powered devices, sensors, motors, and power supplies, and they are the starting point for Kirchhoff's laws, RC circuits, and more detailed electronics. Later topics add complexity, but the same four quantities keep their meanings throughout.