# Understanding combination resistors in series and parallel

In a circuit, resistors can be connected in series or parallel. The total resistance of a group of resistors is determined by their values as well as the way they are connected. A resistor is a component that restricts the flow of charge in a circuit. Most circuits use multiple resistors. The term “resistance” refers to a measurement of this charge flow restriction. The series and parallel connections are the most basic resistor combinations. The total resistance of a group of resistors is determined by their values as well as the way they are connected. A combination circuit can be split down into similar pieces that are either connected in series or connected in parallel.

In this article, you’ll get to know the series and parallel resistors, which is known as combination resistor.

Read more: Different types of resistors

Contents

## Series, Parallel and Combination resistors

### Resistors in series

When you connect resistors in series, the current flowing through each resistance is the same. In other words, in a series circuit, the current is constant at all points. The total voltage (or potential difference) across all resistors is equal to the sum of the voltages across each resistor when resistors are linked in series. To put it another way, the voltages in the circuit add up to the supply voltage. The sum of all the individual resistances in a series of resistors equals the total resistance.

The following is true in this circuit.

I1 = I2 = I3

VT = V1 + V2 + V3

and, RT = R1 + R2 + R3

You should note that the sum of the individual resistances in a circuit with resistors connected in series equals the overall resistance. When the passage of charge, or current, must pass through components in a specific order, resistors are used in series.

#### Diagram of resistors in series: Note: Because if a current was provided at one end, it would flow sequentially through each resistor to the other, these four resistors are linked in series.

A voltage source is connected to a series of resistors in the diagram below. Because the current must flow through each resistor in the circuit in order, the overall resistance in the circuit is equal to the sum of the individual resistances. Three series-connected resistors are connected to a battery (left) and the equivalent single or series resistance (right).

### Calculating Voltage Changes in Series Resistors Using Ohm’s Law

The voltage drops across a resistor while a current flows through it is calculated using Ohm’s law’s equation V=IR, where I is the current in amps (A) and R is the resistance in ohms (Ω).

So V1=IR1 is the voltage drop across R1, V2=IR2 is the voltage drop across R2, and V3=IR3 is the voltage drop across R3. Based on the conservation of energy and charge, the sum of the voltages would be V=V1+V2+V3. When the values for specific voltages are substituted, we get:

V=IR1+IR2+IR3V=IR1+IR2+IR3

or

V=I(R1+R2+R3) V=I(R1+R2+R3)

This means that the sum of the individual resistances in a series equals the total resistance. As a result, for any circuit with N resistors connected in series:

RN(series)=R1+R2+R3+…+RN.RN(series)=R1+R2+R3+…+RN.

Because all of the current must pass through each resistor, it is subjected to its resistance, and series resistances simply build up. Individual resistors in series do not get the total source voltage, but divide it, due to the inverse relationship between voltage and resistance. When two light bulbs are connected in a series circuit with a battery, this is indicated. The light bulb in a basic circuit with one 1.5V battery and one light bulb would have a voltage drop of 1.5V across it. However, if two lightbulbs were connected in series with the same battery, the voltage drop across them would be 1.5V/2, or 0.75V.

Read more: Understanding resistor color codes

The brightness of the lights would reflect this: each of the two light bulbs in series would be half as bright as the single light bulb. As a result, resistors in series consume the same amount of energy as a single resistor, but the energy is distributed among the resistors based on their resistances.

### Resistors in parallel

The supply current is equal to the sum of the currents through each resistor when resistors are connected in parallel. The supply current is equal to the sum of the currents in the parallel circuit’s branches. When resistors are linked in parallel, the potential difference between them is the same. Any parallel components have the same potential difference between them. This equation is used to determine the total resistance of two resistors linked in parallel.

1R=1R1+1R2

We add a third resistor to the equation to compute the total resistance of three resistors linked in parallel (and so on).

1R=1R1+1R2+1R3

When each resistor is connected directly to the voltage source by connecting cables with low resistance, the resistors are in parallel. As a result, the whole voltage of the source is supplied to each resistor.

#### Diagram of resistors in parallel: A set of resistors is connected in parallel.

The current drawn by each resistor is the same as if it were the only resistor connected to the voltage source. This is true of a home’s or apartment’s circuits. Each outlet (or “resistor”) that is connected to an appliance can operate independently, and the current does not have to flow through each appliance in order.

### Parallel Resistors and Ohm’s Law The equivalent single or parallel resistance of three resistors connected in parallel to a battery.

The whole voltage is applied to each resistor in the circuit. The currents flowing through the different resistors are I1=VR1I1=VR1, I2=VR2I2=VR2, and I3=VR3I3=VR3, according to Ohm’s rule. Because of charge conservation, the total current equals the sum of these currents:

I=I1+I2+I3.I=I1+I2+I3.

Substituting individual currents for the expression yields:

I=VR1+VR2+VR3I=VR1+VR2+VR3

or

I=V(1R1+1R2+1R3)I=V(1R1+1R2+1R3)

This means that in a parallel circuit, the overall resistance is equal to the sum of the inverses of each resistance. As a result, for every circuit with an nn number of parallel resistors,

Rn(parallel)=1R1+1R2+1R3…+1Rn.Rn(parallel)=1R1+1R2+1R3…+1Rn.

The total resistance as a result of this relationship is less than the smallest of the individual resistances. When resistors are connected in parallel, more current flows from the source than would flow if they were connected separately, resulting in a lower total resistance.

Each parallel resistor receives the same full voltage from the source, but the total current is divided among them. Connecting two light bulbs in a parallel circuit with a 1.5V battery is one example of this. When connected to a single battery source in a series circuit, the two light bulbs would be half as bright.

The two light bulbs, however, would be just as bright if they were linked in parallel to the battery as if they were connected individually. Because both light bulbs are receiving the same full voltage, the battery will also die more quickly because it is practically delivering full energy to both light bulbs. In a series circuit, the battery lasts the same amount of time as a single light bulb, but the brightness is shared among the lights.

### Resistors in combination circuits

A combination circuit can be split down into similar pieces that are either connected in series or connected in parallel. You should know that more complicated Resistor connections are sometimes only a combination of series and parallel. This is a regular occurrence, especially when wire resistances are taken into account. In this situation, the wire resistance is in series with other parallel resistances. A combination circuit’s many sections can be identified as series or parallel, reduced to their counterparts, and then further reduced until just a single resistance remains. The current and power delivered to a resistor are reduced by wire resistance. When cable resistance is high, such as in a worn (or very long) extension cord, this loss can be severe, affecting power output into appliances.

The circuit of this combination circuit can be divided into two parts: a series component and a parallel component. Two parallel resistors in series with one resistor.

1R1+1R21R1+1R2 or R1R2R1+R2R1R2R1+R2

R3 is connected in series to both R1 and R2, so the resistance would be calculated as:

R=R1R2R1+R2+R3R=R1R2R1+R2+R3

### Complex combination circuits

For more intricate combination circuits, different sections can be identified as series or parallel, reduced to equivalents, and then further reduced until only a single resistance remains, as shown in. The combination of seven resistors in this diagram was detected as being either in series or parallel. The two circular parts in the first illustration represent parallel resistors. Read more: Understanding wire wound resistor

This seven-resistor combo has both series and parallel components. Each one is detected and lowered to an equivalent resistance, which is then decreased further until only one equivalent resistance remains.

We may envision the circuit more clearly by combining those parallel resistors into a single R-value. The circled part in the top right image comprises two resistors connected in series. By combining them, we can get another R-value. The circled two resistors are in parallel in the next step. The latter two are in series, therefore they may be reduced to a single resistance value for the entire circuit by reducing them.

The resistance in wires reduces the current and power given to a resistor, which is one practical aspect of a combination circuit. Based on an understanding of the equivalent resistance of parallel branches of a combination circuit, a combination circuit can be turned into a series circuit. The overall resistance of a circuit can be determined using a series circuit. Wire resistance is connected to the resistor in a series. As a result, the overall resistance rises while the current falls. This loss can be severe if the wire resistance is extremely high, as in a worn (or a very long) extension cord. The IR drop in the wires can be severe if a large current is consumed.