Formulas For Parallel Circuits

Formulas for Parallel Circuits

A parallel circuit is a circuit in which two or more components are connected in parallel. This means that the components are all connected to the same voltage source, but they have their own individual paths to ground. The total current in a parallel circuit is equal to the sum of the currents through each of the individual components. The formula for calculating the total current is: ``` I = I1 + I2 + I3 + ... + In ``` where: *

I

is the total current in the circuit *

I1

I2

I3

, ...,

In

are the currents through each of the individual components The total resistance in a parallel circuit is less than the resistance of any of the individual components. The formula for calculating the total resistance is: ``` 1/R = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn ``` where: *

R

is the total resistance in the circuit *

R1

R2

R3

, ...,

Rn

are the resistances of the individual components The voltage across each of the components in a parallel circuit is the same. This is because all of the components are connected to the same voltage source. The power dissipated by each of the components in a parallel circuit is equal to the product of the current through the component and the voltage across the component. The formula for calculating the power dissipated by a component is: ``` P = IV ``` where: *

P

is the power dissipated by the component *

I

is the current through the component *

V

is the voltage across the component ## Example Let's consider a parallel circuit with three resistors, R1, R2, and R3. The resistors are all connected to a 12-volt battery. The values of the resistors are R1 = 2 ohms, R2 = 4 ohms, and R3 = 6 ohms. The total current in the circuit can be calculated using the following formula: ``` I = I1 + I2 + I3 ``` We can use Ohm's law to calculate the current through each of the resistors: ``` I1 = V/R1 = 12 V / 2 ohms = 6 A I2 = V/R2 = 12 V / 4 ohms = 3 A I3 = V/R3 = 12 V / 6 ohms = 2 A ``` Therefore, the total current in the circuit is: ``` I = I1 + I2 + I3 = 6 A + 3 A + 2 A = 11 A ``` The total resistance in the circuit can be calculated using the following formula: ``` 1/R = 1/R1 + 1/R2 + 1/R3 ``` ``` 1/R = 1/2 ohms + 1/4 ohms + 1/6 ohms = 7/12 ohms ``` Therefore, the total resistance in the circuit is: ``` R = 12 ohms / 7 = 1.71 ohms ``` The voltage across each of the resistors is the same, and it is equal to the voltage of the battery: ``` V = 12 V ``` The power dissipated by each of the resistors can be calculated using the following formula: ``` P = IV ``` ``` P1 = 6 A * 12 V = 72 W P2 = 3 A * 12 V = 36 W P3 = 2 A * 12 V = 24 W ``` Therefore, the total power dissipated by the resistors is: ``` P = P1 + P2 + P3 = 72 W + 36 W + 24 W = 132 W ``` ## Conclusion This article has introduced the formulas for parallel circuits. These formulas can be used to calculate the total current, total resistance, voltage, and power dissipated by a parallel circuit.

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