# Parallel Circuits

A parallel circuit is one in which current can flow through several paths simultaneously.

Notice that unlike a series circuit in this circuit current flows through resistors 1, 2, 3 and 4 simultaneously.

If you stopped the flow of current at any of those resistors, current would still flow through the others. See circuit this concept.

## Parallel Circuit Rules and Formulas

### Total Voltage is the same or the voltage on any resistor. The voltage on all resistors is the same.

Total Voltage = Voltage at resistor 1 = ...Voltage at Resistor

_{ n}V

_{t}= V_{1}+ V_{2}+ ... V_{n}### Total Current is the sum of the individual currents on the different resistors.

Total Current = Current at resistor 1 + Current at resistor 2 + ... Current at Resistor

_{ n}I

_{t}= I_{1}+ I_{2}+ ... I_{n}### Total Inverse Resistance is equal to the sum of the inverses of the individual resistances

Total Inverse Resistance = Inverse Resistance 1 + Inverse Resistance 2 + ... Inverse Resistance

_{ n}## Example 1:

What's the total current and total Voltage for the circuit below?

I

I

I

_{t}= I_{1}+ I_{2}+ I_{3}+ I_{4}I

_{t}= 5A + 10A + 10A + 5AI

_{t}= 30ASince Voltage is the same everywhere in a parallel circuit, the total voltage must be 60V.

## Example 2:

What's the total resistance of the circuit below? There are two ways of solving this problem.

You can use the formula for the total resistance.

1/R

1/R

_{t}= R_{1}+ V_{2}+ R_{2}+ R_{3}+ R_{4}1/R

_{t}= 1/30 + 1/30 + 1/15 + 1/30To add fractions, I must find a common denominator. In this case, it is 9. We know that because 60 is divisible by 4, 12, 30, and 4.

1/R

_{t}= 1/30 + 1/30 + 2/30 + 1/30Notice the third fraction becomes 2/30 instead by 1/30 in order for all fractions to have a common denominator.

1/R

_{t}= 5/30Now, divide both the numerator and the denominator by a number that will turn the numerator into a 1. Let's divide both numbers by 3.

1/R

1/R

R

_{t}= 5 ÷ 5 / 30 ÷ 5 = 1/61/R

_{t}= 1/6R

_{t}= 6Another way of nothing this problem is by using the circuit totals and using ohm's law

First, we calculate the circuit's total current

I

I

_{t}= 2A + 2A + 4A + 2AI

_{t}= 10AThen, we calculate the circuit's total voltage. If we calculate the voltage at any resistance, that will be the total voltage. Let's do it on the first resistance.

V

V

V

V

V

_{1}= I_{1}x R_{1}V

_{1}= 2A x 30 ΩV

_{1}= 60VV

_{t}= V_{1}= ... V_{n}V

_{t}= 60VNow that we know

R

R

R

_{T}= V_{T}/ I_{T}R

_{T}= 60V/10AR

_{T}= 6 Ω
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