Equivalent Resistance Formula

Resistance is the speed breaker that is connected to the circuit to protect it from the high current flow. When we connect two or more resistances in series or in parallel to each other, the security of the circuit increases.

For an electrical circuit, multiple resistors can be arranged in both series and parallel. There is a particular formula to find equivalent resistance for both series and parallel arrangement of resistors about which we will discuss in this article in detail.


What is the Equivalent Resistance?

The equivalent resistance is defined as a common point or node where the total resistance is measured in a series or parallel arrangement (in either the whole circuit or in a fraction of the circuit). 

The equivalent resistance or multiple resistors is defined between two terminals or nodes of the electrical network. Equivalent resistance may sound complicated, but it’s just a technical way to say the sum of the resistance.

In the equivalent resistance of an electrical network, a single resistor can substitute the complete network so that a particular applied voltage or the equivalent current can be obtained similar to the one when utilized as a network.

When a circuit has more than one circuit component in it, there should be a way to calculate the total resistance of the circuit or for a part of the circuit.

Before we discuss what equal resistance is, we can describe the term resistance. 

Resistance is a measure of how much an electrical device or material can resist or obstruct the movement of electric current through it. It is inversely related to current, which means the higher resistance is, the lesser is the current flow; reduced resistance means higher current flow in the circuit.

 

How To Find The Equivalent Resistance?

The equivalent resistance represents the total effect of all resistors connected in the circuit, be it series or in parallel. The equivalent resistance can be measured in either a series or parallel circuit, so the total effect of resistors can also be ascertained by finding the equivalent resistance.

Resistor comprises two junctions through which the current passes in and out. Resistors are passive devices that use electricity

In order to improve the total resistance, the resistors must be connected in series, and to reduce the resistance, the resistors must be connected in parallel. 

 

Series and Parallel Resistance Example

Roads where maximum accidents occur, we can use the series arrangement of resistors to reduce accidents. So, accidents are current flow and the road is an electrical circuit.

In a place where there are fewer chances of an accident, we can use the parallel arrangement of resistors to avoid any mishappening. So, here the road is an electrical circuit and obstruction is the resistance.

 

The Formula of Equivalent Resistance

Now, we will discuss how to determine the resistors connected in a series arrangement by using the formula of equivalent resistance in series and for parallel resistors by using the equivalent resistance parallel formula.


Series Arrangement of Resistance

Let’s suppose that there is a big road, and multiple speed breakers are connected from end-to-end on this road, here, speed breakers are resistors. When resistors are connected in series, the resistors are connected inline end-to-end, the arrangement of such a case is shown in the following diagram:

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The formula to find the equivalent resistance of resistors in series is:

RS = R1 + R2 + R3

So, the equivalent resistance is the sum total of all resistors in series.


The Parallel Arrangement of Resistance

Let’s suppose that there are multiple resistors connected in parallel to each other along the circuit just like speed breakers joined in parallel along the road.

In terms of electrical resistance, the equivalent resistance of resistors in parallel have a reduced effect. The schematic diagram for the parallel arrangement in the circuit is shown below:

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For resistors in parallel, the equivalent resistance formula in parallel is:

1/RP = 1/R1 + 1/R2 + ….+ 1/Rn

So, the net effect of resistance in a parallel arrangement, as we can see in the above equivalent resistance equation.


Formula to Find Equivalent Resistance

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In this question, we will determine the equivalent resistance of resistors connected in the above arrangement.

Starting from point A, 1Ω and 1Ω are connected in parallel, so the formula to find the equivalent resistance is:

1/1 + 1/1 = 2/1 

So, the equivalent resistance is ½ Ω.

Now, 2 and 1 are connected in parallel, so the equivalent resistance is:

½ + 1/1 = 3/2 

So, the equivalent resistance is ⅔ Ω.

Now, 2/3 and 1 are connected in parallel again, so the equivalent resistance formula for resistors in parallel is:

3/2 + 1/1 = 5/2

So, the equivalent resistance is ⅖ Ω.

Now, lastly, 2/5 and 1 are in parallel, so the equivalent resistance is:

5/2 + 1/1 = 7/2

So, the equivalent resistance is 3 (½) Ω.

FAQs (Frequently Asked Questions)

Question 1: What is the Equivalent Resistance of the Network? What is the Equivalent Resistance (RT)?

Answer: We define the equivalent resistance of an electrical network as a single resistor that can substitute the entire network in a way that for an applied voltage ‘V’, we get the same current ‘I’ as we get for a network. The equivalent resistance can be calculated by using the following arrangements:

  • Series arrangement

  • Parallel arrangement

To determine the equivalent resistance (RT), we need to upside-down our result. Here, we use a device called the Meter Bridge to accurately calculate the equivalent effective resistance. The Meter Bridge is a device that is used for the measurement of resistance using the phenomenon of Wheatstone Network.

Question 2: What is Resistance? How the Resistance Differs from the Equivalent Resistance?

Answer: Resistance is the opposition that a material offers to the flow of electric current through it.

It is represented by the uppercase letter R. The standard unit of resistance is the ohm, sometimes written out as a word, and sometimes we symbolize it by the uppercase Greek letter omega (Ω). 

The term resistance refers to the way we measure or determine how much a circuit component resists the flow of electricity, or current, passing through it. More resistance means less current flows through the circuit and vice-versa. The equivalent resistance is a different way of indicating 'total effective’ resistance, which we calculate differently for series and parallel circuits.