# Equation For Power Parallel Circuits In Series And

## Equation for Power in Parallel Circuits

In a parallel circuit, the voltage across each resistor is the same, but the current through each resistor is different. The total current in a parallel circuit is equal to the sum of the currents through each resistor. The equation for power in a parallel circuit is given by: ``` P = IV ``` where: * P is the power in watts * I is the current in amps * V is the voltage in volts The total power in a parallel circuit can be calculated by adding the power dissipated by each resistor: ``` Ptotal = P1 + P2 + P3 + ... + Pn ``` where: * Ptotal is the total power in watts * P1, P2, P3, ..., Pn are the powers dissipated by each resistor in watts ## Example Consider a parallel circuit with three resistors, R1 = 10 ohms, R2 = 20 ohms, and R3 = 30 ohms. The voltage across the circuit is 12 volts. The current through each resistor can be calculated using Ohm's law: ``` I1 = V / R1 = 12 V / 10 ohms = 1.2 amps I2 = V / R2 = 12 V / 20 ohms = 0.6 amps I3 = V / R3 = 12 V / 30 ohms = 0.4 amps ``` The total current in the circuit is: ``` Itotal = I1 + I2 + I3 = 1.2 amps + 0.6 amps + 0.4 amps = 2.2 amps ``` The total power dissipated by the circuit is: ``` Ptotal = P1 + P2 + P3 = (1.2 amps)^2 * 10 ohms + (0.6 amps)^2 * 20 ohms + (0.4 amps)^2 * 30 ohms = 14.4 watts ``` ## Applications Parallel circuits are used in a variety of applications, including: * Electrical distribution systems * Power supplies * Audio amplifiers * Lighting circuits * Computer circuits Parallel circuits are often used to increase the current capacity of a circuit without increasing the voltage. For example, a parallel circuit with two 10-ohm resistors can provide the same current as a single 20-ohm resistor. This is because the total resistance of a parallel circuit is less than the resistance of any individual resistor. Parallel circuits can also be used to increase the voltage tolerance of a circuit. For example, a parallel circuit with two 10-volt batteries can provide a voltage of up to 20 volts without damaging the circuit. This is because the total voltage of a parallel circuit is greater than the voltage of any individual battery. ## Conclusion Parallel circuits are a versatile and powerful tool that can be used in a variety of applications. By understanding the principles of parallel circuits, you can design and build circuits that meet your specific needs.

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