Coulombs (c) to Millicoulombs (mC) conversion

What is Coulombs?

The coulomb (symbol: C) is the standard unit of electrical charge in the International System of Units (SI). It represents the amount of charge transported by a current of one ampere flowing for one second. Understanding the coulomb is fundamental to comprehending electrical phenomena.

Definition and Formation

One coulomb is defined as the quantity of charge that is transported in one second by a steady current of one ampere. Mathematically:

$1 \ C = 1 \ A \cdot 1 \ s$

Where:

• C is the coulomb
• A is the ampere
• s is the second

At the atomic level, the coulomb can also be related to the elementary charge ($e$), which is the magnitude of the electric charge carried by a single proton or electron. One coulomb is approximately equal to $6.241509 \times 10^{18}$ elementary charges.

$1 \ C \approx 6.241509 \times 10^{18} \cdot e$

Coulomb's Law and Charles-Augustin de Coulomb

The unit "coulomb" is named after French physicist Charles-Augustin de Coulomb (1736–1806), who formulated Coulomb's Law. This law quantifies the electrostatic force between two charged objects.

Coulomb's Law states that the electric force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. The formula is:

$F = k \cdot \frac{|q_1 \cdot q_2|}{r^2}$

Where:

• $F$ is the electrostatic force (in Newtons)
• $k$ is Coulomb's constant ($k \approx 8.98755 \times 10^9 \ N \cdot m^2/C^2$)
• $q_1$ and $q_2$ are the magnitudes of the charges (in Coulombs)
• $r$ is the distance between the charges (in meters)

For a deeper dive into Coulomb's Law, refer to Hyperphysics's explanation

Real-World Examples of Coulomb Quantities

Understanding the scale of a coulomb requires some perspective. Here are a few examples:

• Static Electricity: The static electricity you experience when touching a doorknob after walking across a carpet involves charges much smaller than a coulomb, typically on the order of nanocoulombs ($10^{-9} \ C$) to microcoulombs ($10^{-6} \ C$).

• Lightning: Lightning strikes involve massive amounts of charge transfer, often on the order of several coulombs to tens of coulombs.

• Capacitors: Capacitors store electrical energy by accumulating charge on their plates. A typical capacitor might store microcoulombs to millicoulombs ($10^{-3} \ C$) of charge at a given voltage. For example, a 100µF capacitor charged to 12V will have 0.0012 Coulombs of charge.

  $Q = C \cdot V$

  Where:

  • Q is the charge in Coulombs
  • C is the capacitance in Farads
  • V is the voltage in Volts

• Batteries: Batteries provide a source of electrical energy by maintaining a potential difference (voltage) that can drive a current. The amount of charge a battery can deliver over its lifetime is often rated in Ampere-hours (Ah). One Ampere-hour is equal to 3600 Coulombs (since 1 hour = 3600 seconds). Therefore, a 1 Ah battery can theoretically supply 1 Ampere of current for 1 hour, or 3600 Coulombs of charge in that hour.

What is Millicoulombs?

Millicoulombs (mC) are a unit of electrical charge, a fundamental property of matter. Understanding what millicoulombs represent helps in grasping electrical phenomena and calculations.

Definition of Millicoulombs

A millicoulomb (mC) is a subunit of the coulomb (C), the standard unit of electrical charge in the International System of Units (SI). "Milli-" indicates a factor of one-thousandth, meaning:

$1 \, \text{mC} = 0.001 \, \text{C} = 1 \times 10^{-3} \, \text{C}$

How Millicoulombs Relate to Coulombs

The relationship is straightforward: one coulomb is equal to one thousand millicoulombs. This makes millicoulombs convenient for expressing smaller quantities of charge.

$1 \, \text{C} = 1000 \, \text{mC}$

Connection to Coulomb's Law

Coulomb's Law quantifies the electrostatic force between charged objects. While the law uses coulombs as the unit of charge, millicoulombs can be readily used if you adjust the units accordingly. Coulomb's Law states:

$F = k \frac{|q_1 q_2|}{r^2}$

Where:

• $F$ is the electrostatic force.
• $k$ is Coulomb's constant (approximately $8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$).
• $q_1$ and $q_2$ are the magnitudes of the charges.
• $r$ is the distance between the charges.

Real-World Examples and Applications

While the coulomb is a large unit, millicoulombs are more practical for describing charges in common applications.

• Electrostatic discharge (ESD): The charge transferred during an ESD event (like a static shock) can be on the order of millicoulombs or even microcoulombs.
• Capacitors: Small capacitors used in electronics store charge. The amount of charge stored is often expressed in microcoulombs or millicoulombs. For example, a 100 microfarad capacitor charged to 5 volts stores $Q = CV = (100 \times 10^{-6} F)(5 V) = 500 \times 10^{-6} C = 0.5 \, \text{mC}$.
• Batteries: The capacity of a battery is often rated in milliampere-hours (mAh). The total charge a battery can deliver can be calculated. For example, a battery rated at 2000 mAh can deliver a charge of $Q = It = (2 A)(3600 s) = 7200 C$.

Charles-Augustin de Coulomb

Charles-Augustin de Coulomb (1736-1806) was a French physicist who formulated Coulomb's Law. His work laid the foundation for the quantitative study of electrostatics and magnetism. His meticulous experiments with torsion balances led to the precise determination of the force law governing the interaction of electric charges. For more information, you can refer to Charles-Augustin de Coulomb in Britannica website.