Electric charge is a fundamental concept in physics, essential for understanding electromagnetism and electrical systems. Whether you are working with batteries, capacitors, or circuits, it’s important to know how to convert between different units of electric charge. In this guide, we’ll explore the most common units of electric charge, explain their definitions, and show you how to convert between them.

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What is Electric Charge?

Electric charge is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge:

• Positive charge (e.g., protons)
• Negative charge (e.g., electrons)

The unit of electric charge in the International System of Units (SI) is the coulomb (C). The elementary charge (e), which is the charge of a single electron or proton, is approximately 1.602 x 10⁻¹⁹ C.

Electric charge plays a crucial role in many phenomena, including electric currents, electromagnetic radiation, and chemical reactions.

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Common Units of Electric Charge

1. Coulomb (C)

• The coulomb (C) is the standard unit of electric charge in the SI system.
• 1 coulomb is the charge transported by a current of 1 ampere flowing for 1 second.
• Formula:
  Q = I × t, where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds.

2. Electron Charge (e)

• The electron charge (e) is the charge of a single electron or proton.
• The value of e is approximately 1.602 x 10⁻¹⁹ C.

3. Ampere-Hour (Ah)

• Ampere-hour (Ah) is a unit of electric charge commonly used to describe battery capacity.
• 1 Ah is the charge transferred by a current of 1 ampere flowing for 1 hour.
• 1 Ah = 3600 C, since 1 hour = 3600 seconds.

4. Milliampere-Hour (mAh)

• Milliampere-hour (mAh) is a smaller unit of charge, commonly used for smaller batteries like those in smartphones.
• 1 mAh = 10⁻³ Ah = 3.6 C.

5. Faraday (F)

• The Faraday (F) is a unit of electric charge equal to the charge of one mole of electrons.
• 1 F ≈ 96,485 C (known as the Faraday constant).

6. Nanocoulomb (nC)

• The nanocoulomb (nC) is a subunit of the coulomb.
• 1 nC = 10⁻⁹ C.

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How to Convert Between Electric Charge Units

Here’s a guide on how to convert between the common units of electric charge.

1. Coulombs to Electron Charges (e)

• 1 e = 1.602 x 10⁻¹⁹ C.
• To convert from coulombs to electron charges, divide the value in coulombs by 1.602 x 10⁻¹⁹.
• Example: To convert 3.204 x 10⁻¹⁸ C to electron charges:
  • 3.204 x 10⁻¹⁸ C ÷ 1.602 x 10⁻¹⁹ C/e = 2 e.

2. Coulombs to Ampere-Hours (Ah)

• 1 Ah = 3600 C.
• To convert from coulombs to ampere-hours, divide the value in coulombs by 3600.
• Example: To convert 7200 C to Ah:
  • 7200 C ÷ 3600 C/Ah = 2 Ah.

3. Ampere-Hours to Coulombs

• 1 Ah = 3600 C.
• To convert from ampere-hours to coulombs, multiply the value in ampere-hours by 3600.
• Example: To convert 3 Ah to coulombs:
  • 3 Ah × 3600 C/Ah = 10,800 C.

4. Coulombs to Milliampere-Hours (mAh)

• 1 mAh = 3.6 C.
• To convert from coulombs to milliampere-hours, divide the value in coulombs by 3.6.
• Example: To convert 180 C to mAh:
  • 180 C ÷ 3.6 C/mAh = 50 mAh.

5. Faradays to Coulombs

• 1 F ≈ 96,485 C.
• To convert from faradays to coulombs, multiply the value in faradays by 96,485.
• Example: To convert 2 F to coulombs:
  • 2 F × 96,485 C/F = 192,970 C.

6. Nanocoulombs to Coulombs

• 1 nC = 10⁻⁹ C.
• To convert from nanocoulombs to coulombs, divide the value in nanocoulombs by 10⁹.
• Example: To convert 500 nC to coulombs:
  • 500 nC ÷ 10⁹ = 5 x 10⁻⁷ C.

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Electric Charge Unit Conversion Table

Here’s a quick reference table to help you convert between electric charge units:

From	To	Conversion Factor	Example
Coulombs (C)	Electron Charge (e)	1 e = 1.602 x 10⁻¹⁹ C	3.204 x 10⁻¹⁸ C = 2 e
Coulombs (C)	Ampere-Hours (Ah)	1 Ah = 3600 C	7200 C = 2 Ah
Ampere-Hours (Ah)	Coulombs (C)	1 Ah = 3600 C	3 Ah = 10,800 C
Coulombs (C)	Milliampere-Hours (mAh)	1 mAh = 3.6 C	180 C = 50 mAh
Faradays (F)	Coulombs (C)	1 F = 96,485 C	2 F = 192,970 C
Nanocoulombs (nC)	Coulombs (C)	1 nC = 10⁻⁹ C	500 nC = 5 x 10⁻⁷ C

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Applications of Electric Charge Conversion

Converting between units of electric charge is important in several fields:

1. Electronics: When designing circuits or evaluating battery capacity, understanding the charge in ampere-hours (Ah) or milliampere-hours (mAh) is essential.
2. Physics: In electromagnetism, calculating the force between charges or the behavior of electric fields often requires working with coulombs (C) or faradays (F).
3. Battery Technology: Batteries are typically rated in Ah or mAh, and converting these to coulombs (C) helps understand the total charge storage.
4. Electrochemistry: When studying electrochemical reactions or processes like electroplating, knowing how much charge flows is essential for determining material deposition or reaction rates.