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How to compute capacitor voltage by energy in Python using UliEngineering

You can easily compute the voltage required to store a specific amount of energy in a capacitor using the UliEngineering Python library:

capacitor_voltage_by_energy.py
from UliEngineering.Electronics.Capacitors import capacitor_voltage_by_energy
from UliEngineering.EngineerIO import *

# Compute voltage for 100µF to store 1mJ
voltage = capacitor_voltage_by_energy("100uF", "1mJ")
print(f"Voltage for 1mJ in 100µF: {format_value(voltage, 'V')}")

# Compute voltage for 1nF to store 72nJ
voltage = capacitor_voltage_by_energy("1nF", "72nJ")
print(f"Voltage for 72nJ in 1nF: {format_value(voltage, 'V')}")

Example output

capacitor_voltage_by_energy_output.txt
Voltage for 1mJ in 100µF: 4.47 V
Voltage for 72nJ in 1nF: 12.0 V

This calculation determines the voltage needed to store a specific amount of energy in a capacitor. This is useful for power supply design, energy storage calculations, and determining the voltage requirements for pulse circuits. The relationship shows that voltage increases with the square root of the energy for a given capacitance.

The voltage is computed using the formula: $V = \sqrt{\frac{2E}{C}}$, where $V$ is the voltage in volts, $E$ is the energy in joules, and $C$ is the capacitance in farads. This is derived from the energy formula $E = \frac{1}{2} C V^2$, rearranged to solve for voltage.

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