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Light Emitting Diodes (LEDs) are commonly used in various electronic devices due to their low energy usage and long lifespan. Calculating the resistance of a parallel resistor in an LED circuit is critical in ensuring the LED operates safely and efficiently without being overpowered. This involves factors such as supply voltage, LED color (which affects LED voltage), LED current, and the number of LEDs in the circuit. This topic is of particular relevance to electrical engineering and physics.

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The resistance for a parallel resistor in an LED circuit can be calculated using Ohm's law and the following formula:

R = (Vs - Vled) / Iled

Where:

- R is the resistance of the parallel resistor.
- Vs is the supply voltage.
- Vled is the LED voltage, which varies depending on the color of the LED.
- Iled is the current through the LED, typically in the range of 5-20 milliamperes.

While Ohm's law, the fundamental principle used in this calculation, was first formulated by Georg Simon Ohm in 1827, the specific usage of the formula for calculating the resistance in LED circuits has been developed over time with the growth of semiconductor technology and electronics. This formula is fundamental to electrical engineering, particularly in the design of LED circuits, and also finds its application in physics when dealing with electricity and magnetism.

The formula and principles explained are used extensively in designing and manufacturing LED lighting systems, display boards, traffic signals, and numerous other electronic devices. Understanding and applying this formula ensures that these devices operate effectively and safely.

Georg Simon Ohm, who formulated Ohm's law, is a key figure in the understanding and calculation of electrical resistance. His discoveries have provided the foundation for countless advances in electrical engineering and physics.

- The voltage drop across an LED is dependent on its color. For example, red LEDs typically have a voltage drop of about 1.8V, while blue LEDs can have a voltage drop of around 3.6V.
- The proper calculation and usage of resistors in LED circuits not only ensures efficient operation but also significantly increases the lifespan of the LEDs.
- The development and popularization of LED technology has greatly reduced energy consumption for lighting worldwide, contributing to sustainability efforts.

Understanding how to calculate the resistance for a parallel resistor in an LED circuit is fundamental to the fields of electrical engineering and physics. The practical applications of these calculations are wide-ranging, underscoring the importance of this knowledge in the design and manufacture of a variety of LED-based electronic devices.

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