# Simplified Formulas for Parallel Circuit Resistance Calculations # Simplified Formulas for Parallel Circuit Resistance Calculations

Calculating the equivalent resistance (REQ) of parallel resistors by hand is time-consuming. This tool was created to assist you in rapidly calculating the equivalent resistance of up to six parallel resistors. Simply define the number of parallel resistors and their resistance values to utilize it.

If you have more than six resistors, just use the calculator to calculate the equivalent resistance of the first six, then enter that value into R1 and add values for R7, R8,…, R11 into the R2, R3,…, R6 input sections of the calculator. An electrical circuit is a series of electrical elements connected by a closed loop. Electrons can flow freely between the electrical elements in a closed loop. We’ll now go through how to use voltage, current, and resistance to examine simple electrical circuits.

When two or more components are linked in parallel, the potential difference (voltage) across their ends is the same. The magnitude of the potential differences between the components is the same, and their polarities are likewise the same. All circuit components connected in parallel receive the same voltage. According to Kirchhoff’s current law, the total current is the sum of the currents flowing through the constituent components.

The Shunt Application is a basic application of these connection strategies. In the electric measuring industry, we frequently need to measure extremely high currents and voltages (in the range of 500kV upwards). The issue is that metering devices are made up of delicate electronic components with low voltage and current ratings.

### Voltage

The voltage across all elements in a parallel circuit is the same. ### Current

Ohm’s law determines the current in each individual resistor. When you subtract the voltage, you get ### Resistance units

To calculate the overall resistance of all components, add the reciprocals of each component’s resistances R iR i and take the reciprocal of the sum. The total resistance will always be smaller than the least resistance value.

The battery voltage will be the same as the cell voltage if the cells are linked in parallel, but the current supplied by each cell will be a percentage of the overall current. For instance, if a battery has four identical cells linked in parallel and delivers one ampere of current,

Each cell will provide 0.25 ampere of electricity. If the cells aren’t identical, higher-voltage cells will try to charge lower-voltage cells, perhaps harming them.

The current in a parallel circuit is separated at junctions before proceeding along a different channel.
In a Parallel Circuit, switches are used to allow current to flow down one path at a time.
The Potential Difference between components that are arranged in parallel has the same value.

The overall current flow in a parallel circuit is equal to the sum of the currents flowing through each branch.

Because the supply current might travel in many directions, the current may not be the same along all of the parallel network’s branches. In a parallel resistive network, however, the voltage drop across all of the resistors is the same. Then, all parallel linked elements have a common voltage across them, and this is true for all resistors in parallel.

A parallel resistive circuit is defined as one in which the resistors are linked to the same two points (or nodes) and is distinguished by the presence of several current paths connecting to a shared voltage source. The voltage across resistor R1 equals the voltage across resistor R2, which equals the voltage across R3, which equals the voltage across R4 and ultimately equals the voltage across R5. In a parallel circuit, the total resistance is equal to the resistance of one resistor divided by the number of resistors. ### Example:

Five lamps, each with a resistance of 40Ω, are connected in parallel. Find total resistance.

Solution :

R1 = R2 = R3 = R4 = R5 = 40Ω

So, N = 5 RT = R / N = 40/5 = 8 Ω

When two parallel circuit resistors are uneven, it is easier to compute RT by multiplying the two resistances and then dividing the product by the sum, as indicated in the equation below. Above equation, this is valid when there are only two resistors in parallel.

### Example:

Find the total resistance of a parallel circuit which has one 12Ω and one 4Ω resistor.

Solution : ### RT = (12 x 4) / (12+4) = 48/16 = 3 Ω

In some circumstances involving two parallel resistors, it is necessary to locate an unknown resistor, Rx, in order to derive a specific RT. To determine the correct formula, start with the previous equation and change R to Rx for the known and unknown resistors. ### Example:

What value of resistance must be added, in parallel, with an 8Ω resistor to provide a total resistance of 6Ω (Figure 28)? Solution :

## Applications

Resistors in series are comparable to a single resistor with a resistance equal to the sum of each individual resistor’s resistance. Parallel resistors, on the other hand, provide an equivalent resistance that is always lower than the resistance of each individual resistor. This makes sense if you think about it: A specific amount of current flows when a voltage is applied across a resistor. When you connect a second resistor in series with the first, you’ve effectively created a new channel through which additional current may flow.

The overall current flowing from the power source will be at least somewhat larger than the current via the single resistor, regardless of how large the second resistor is. The overall resistance must be lower if the total current is larger.