Coulomb

The coulomb ($\mathrm{C}$) is the derived SI unit for electric Charge.

It is defined through current and time:

$$1\mathrm{C}=1\mathrm{A}\mathrm{s}$$

So if a current of one Ampere flows for one Second, one coulomb of charge has passed a point.

The elementary charge is fixed exactly as:

$$e=1.602176634\times 10^{-19}\mathrm{C}$$

Therefore one coulomb corresponds to about:

$$\frac{1}{1.602176634\times 10^{-19}}\approx 6.24\times 10^{18}$$

proton charges, or the same number of electron charges in magnitude.

Important subtlety: charge is quantised in units of $e$, but the coulomb is a macroscopic unit. A real object cannot have exactly arbitrary real-valued charge; it has an integer multiple of $e$. One coulomb is so large that this discreteness is usually invisible in circuit problems.

Useful energy connection:

$$E=QV$$

Moving $1\mathrm{C}$ through $1\mathrm{V}$ transfers $1\mathrm{J}$. That is the bridge from Coulomb and Volt to Joule.

Quick check: current is the rate of charge flow, so $Q=It$. Ten seconds at $0.2\mathrm{A}$ moves $2\mathrm{C}$.

Quick check

Because $1\mathrm{C}=1\mathrm{A}\mathrm{s}$, a current of $0.5\mathrm{A}$ flowing for $10\mathrm{s}$ transfers

$$Q=It=5\mathrm{C}.$$

This is often the easiest way to remember the unit: coulomb = amount of charge, ampere = rate of charge flow.