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Convert energy in joules (J) to voltage in volts (V) given the charge in coulombs. Essential for capacitor and electrical energy calculations.
1 coulomb = 1 amp × 1 second
Where V is voltage in volts, J is energy in joules, and C is charge in coulombs.
A capacitor stores 50 joules of energy with a charge of 5 coulombs:
V = 50 ÷ 5 = 10 volts
| Joules | 0.1 C | 0.5 C | 1 C | 5 C | 10 C |
|---|---|---|---|---|---|
| 1 J | 10 V | 2 V | 1 V | 0.2 V | 0.1 V |
| 5 J | 50 V | 10 V | 5 V | 1 V | 0.5 V |
| 10 J | 100 V | 20 V | 10 V | 2 V | 1 V |
| 50 J | 500 V | 100 V | 50 V | 10 V | 5 V |
| 100 J | 1000 V | 200 V | 100 V | 20 V | 10 V |
| 500 J | 5000 V | 1000 V | 500 V | 100 V | 50 V |
| 1000 J | 10000 V | 2000 V | 1000 V | 200 V | 100 V |
Joules to volts conversion calculates the electrical potential difference (voltage) from a known amount of energy and charge. The fundamental relationship is V = J ÷ C, where V is voltage in volts, J is energy in joules, and C is electrical charge in coulombs. This relationship stems from the definition of a volt itself—one volt equals one joule per coulomb. The conversion is essential in capacitor circuit analysis, battery technology, and energy storage systems. For capacitors specifically, the energy stored follows E = ½CV², requiring a different approach when working with capacitance values. Understanding this conversion helps engineers and physicists calculate how much electrical potential a system can generate from stored energy, which is fundamental to power electronics, defibrillator design, flash photography circuits, and pulsed power systems used in scientific research per IEEE standards.
Measure or calculate the energy in joules. For electrical circuits, energy can be found from power and time (E = P × t) or from capacitor parameters (E = ½CV²).
Calculate charge using Q = I × t (current multiplied by time). For a 3A current flowing for 10 seconds, Q = 30 coulombs. For capacitors, Q = C × V.
Divide the energy in joules by the charge in coulombs. For example, 240 joules with 20 coulombs of charge: V = 240 ÷ 20 = 12 volts.
Check your result against known values. A standard AA battery provides about 1.5V, a car battery 12V, and household outlets 120V or 240V. Ensure the result is reasonable for your application.
Engineers use energy-to-voltage relationships to size capacitors for flash circuits, defibrillators, and pulsed laser power supplies where precise energy delivery at a specific voltage is required.
Understanding the energy-voltage-charge relationship helps evaluate battery capacity, state of charge, and the voltage available from different battery chemistries.
The joule-volt-coulomb relationship is foundational in physics education, connecting the concepts of energy, potential difference, and electric charge in a clear, quantitative way.
| Source | Voltage (V) | Typical Charge (C) | Energy (J) |
|---|---|---|---|
| AAA Battery | 1.5 V | 4,320 C | 6,480 J |
| AA Battery | 1.5 V | 9,360 C | 14,040 J |
| 9V Battery | 9 V | 1,800 C | 16,200 J |
| Car Battery (12V) | 12 V | 180,000 C | 2,160,000 J |
| Camera Flash Capacitor | 300 V | 0.1 C | 30 J |
| Defibrillator | 1,000–5,000 V | 0.04–0.2 C | 150–360 J |
Values are approximate and vary by manufacturer. Battery charge assumes typical mAh capacity converted to coulombs.
Energy (joules) is the total capacity to do work, while voltage (volts) is the energy per unit charge—the electrical "pressure" that drives current through a circuit. You need both energy and charge to determine voltage. A high-energy source with a large charge may have low voltage, while a small charge with the same energy yields high voltage.
For capacitors, use V = √(2E ÷ C), where E is energy in joules and C is capacitance in farads. This derives from the capacitor energy formula E = ½CV². For example, a 100 μF capacitor storing 0.5 J has V = √(2 × 0.5 ÷ 0.0001) = 100 volts.
Defibrillators need to deliver 150–360 joules of energy in a few milliseconds to reset the heart rhythm. High voltage (1,000–5,000V) allows this energy to be delivered quickly through the chest impedance (typically 50–100 Ω). The capacitor stores energy at high voltage and discharges it in a controlled waveform.
An electron volt is the kinetic energy gained by a single electron accelerating through a potential difference of one volt. It equals 1.602 × 10⁻¹⁹ joules. Electron volts are used in particle physics and semiconductor physics because joules would produce inconveniently small numbers at the atomic scale.
Standard multimeters measure voltage, current, and resistance, not energy directly. To determine energy in joules, you must measure voltage and current over time, then calculate E = V × I × t. Some power analyzers and energy meters can display energy readings directly in joules or watt-hours.