Your Cart

Parallel Circuits

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

”ParallelCircuit
circuit with 4 resistors

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_Xout”
interruption of flow through a branch in a parallel circuit. Does NOT affect the other branches
”Parallel_Circuit_5_resistors”
”Parallel_Circuit_branch”

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
Vt = V1 + V2 + ... Vn

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
It = I1 + I2 + ... In

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?
”Parallel_circuits_121_ex1”
It = I1 + I2 + I3 + I4
It = 5A + 10A + 10A + 5A
It = 30A

Since 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.
”Parallel_circuit_ex2131”
You can use the formula for the total resistance.
1/Rt = R1 + V2 + R2 + R3 + R4
1/Rt = 1/30 + 1/30 + 1/15 + 1/30

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/Rt = 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/Rt = 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/Rt = 5 ÷ 5 / 30 ÷ 5 = 1/6
1/Rt = 1/6
Rt = 6

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
It = 2A + 2A + 4A + 2A
It = 10A

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.

V1 = I1 x R1
V1 = 2A x 30 Ω
V1 = 60V
Vt = V1 = ... Vn
Vt = 60V

Now that we know
RT = VT / IT
RT = 60V/10A
RT = 6 Ω
Details
Written by Yanis O.

Add comment