# How to Calculate Coulombs

by Allan Robinson

The coulomb is a measure of electrical charge and is named after Charles-Augustin de Coulomb. Electrons may be treated as an electrical charge so the coulomb is a count of electrons and is therefore a dimensionless unit. The coulomb was the base unit of electrical measure until the Standards Institute (SI) made the ampere the base unit of electrical measure in 1960. The coulomb may easily be calculated from the current in an electrical circuit and the time that the circuit is closed.

Define the coulomb as the amount of electrical charge that 1 ampere transports in a second. This may be expressed as 1 C = 1 A x 1 s and makes the coulomb equal to approximately 6.24 x 10^18 electrons.

Examine an equivalent definition of the coulomb as the charge stored by a one farad capacitance with an electrical potential of one volt. This can be shown mathematically as 1C = 1F x 1V.

Use the definition of coulomb to calculate coulombs from current and time. We then have C = As where C is the charge in coulombs, A is the current in amperes and s is the time in seconds.

Express Coulomb's law. This is given as F = kq1q2/r^2 where F is the force exerted on charges q1 and q2, k is Coulomb's constant (8.987 x 10^9 newton square meters/coulombs squared) and r is the distance separating q1 and q2.

Solve for coulombs using Coulomb's law in Step 4 with q1 and q2 equal. We have F = kq1q2/r^2 => F/k = q^2/r^2 => q^2 = r^2 (F/k) => q = r (F/k)^(1/2).

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