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.

Total Voltage = Voltage at resistor 1 = ...Voltage at Resistor_{ n}

V_{t} = V_{1} + V_{2} + ... V_{n}

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 = Inverse Resistance 1 + Inverse Resistance 2 + ... Inverse Resistance_{ n}

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

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

I_{t} = 5A + 10A + 10A + 5A

I_{t} = 30A

I

I

Since Voltage is the same everywhere in a parallel circuit, the total voltage must be 60V.

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

1/R_{t} = 1/30 + 1/30 + 1/15 + 1/30

1/R

To 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 + 1/30

Notice the third fraction becomes 2/30 instead by 1/30 in order for all fractions to have a common denominator.

1/R_{t} = 5/30

Now, 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_{t} = 5 ÷ 5 / 30 ÷ 5 = 1/6

1/R_{t} = 1/6

R_{t} = 6

1/R

R

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

I_{t} = 10A

I

Then, 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_{1} = I_{1} x R_{1}

V_{1} = 2A x 30 Ω

V_{1} = 60V

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

V_{t} = 60V

V

V

V

V

Now that we know

R_{T} = V_{T} / I_{T}

R_{T} = 60V/10A

R_{T} = 6 Ω

R

R

- Details
- Written by Yanis O.

Office Hours of Operation: Monday - Friday 8:30 AM - 4:30 PM Eastern Time | 866-986-7978

©
2007 - 2023
Contractor Campus, Inc. | All Rights Reserved | 1943 Colonial Blvd Fort Myers FL 33907