## What are Resistors in Parallel : Working & Its Applications

- Frank
- May 25, 2022
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We know that electrical and electronic circuits can be built with more than one electrical and electronic component. In that, a resistor is an essential component because it plays a key role in limiting the current flow within the circuit. A measure of this current flow limit is known as resistance. The combinations of resistors in a circuit are available in two ways like resistors in series and **resistors in parallel**. But the whole resistance of these two combinations mainly depends on both their values & how they are connected in a circuit. So, this article discusses one of the resistors combinations like resistors in parallel with circuits and applications.

### Definition of Resistors in Parallel

Resistors in parallel connection can be defined as, whenever two or more resistors are connected to the two same nodes then it has above one path for current flow that is commonly connected to a single voltage source. Resistors in a parallel circuit, the current flows through above one path because there are several paths available for the current flow.

Since there are several current supply paths in the parallel network, the flow of current is not the same for all the branches but, the voltage drop will be the same across all the parallel-connected resistors in a network. So, this circuit has a common voltage across the resistors. The **resistors in the parallel symbol** are shown below.

### Resistors in Parallel Circuit Diagram

The resistors in a parallel connection circuit are shown below. In the following circuit, three resistors are connected in parallel connections. So the voltage drop across the R1 resistor is equal to the voltage drop across the R2 resistor & similarly across the R3 resistor.

In the above circuit, voltage supply ‘VAB’ will be in between the two points like A & B. Once the three resistors like R1, R2 & R3 are connected in parallel combination then the voltage drop across every resistor is the same. So,

**V _{AB} = V_{R1 }= V_{R2} = V_{R3.}**

Where

‘V_{AB}’ is the voltage supply between A & B nodes.

‘V_{R1}’ is the voltage drop across the R1 resistor.

‘V_{R2}’ is the voltage drop across the R2 resistor.

‘V_{R3}’ is the voltage drop across the R3 resistor.

But the flow of current through this circuit is not the same. If the flow of current ‘I’ leaves node ‘A’ then the current ‘I’ will have three paths to arrive at node B.

The flow of current in every resistor is not independent of its resistance. Thus resistors in connection circuits, the flow of current is not similar within all the three resistors. If the current ‘I1’ flows throughout the R1 resistor, then-current ‘I2’ flows throughout the R2 resistor & ‘I3’ current flows throughout the ‘R3’ resistor.

#### Resistors in Parallel Derivation

So according to KCL (Kirchhoff’s Current Law), the entering current at one node in the circuit is equivalent to leaving current at other nodes.

Thus, **I = I1 + I2 + I3.**

From Ohms law, we know that **V = IR => I = V/R**

**So, I1 = V/R1**

**I2 = V/R2**

**I3 = V/R3**

If the total resistance of the above circuit is ‘RT’ then

I = V / RT

So, V/RT = V/R1+V/R2+V/R3

V(1/RT )= V(1/R1+1/R2+1/R3)

1/RT = 1/R1+1/R2+1/R3

If the equivalent resistance of the above circuit is ‘‘Req’ then it is calculated by including the equal values of separate resistances (1/R). So, the equation of equivalent resistance ‘Req’ for n **resistors in the parallel formula** is shown below.

**(1/Req) = (1/R1) + (1/R2) + (1/R3) + ……… + (1/Rn)**

From the above equation, we can observe that the equal resistance of ‘n’ resistors connected in parallel combination is always lesser as compared to the resistance of the least resistor. If two resistors are connected in parallel, then the equal resistance can be written as

**1/Req = 1/R1 + 1/R2 => Req = R1 * R1 / (R1 + R2)**

If two resistors are connected in parallel combination with equal resistance ‘R’ then the combination of equivalent resistance is ‘R/2’.

Likewise, if 3 resistors are connected with equivalent resistance ‘R’ in parallel then the combination of equivalent resistance is ‘R/3.

Here, the conductance value can be obtained through the parallel connection of resistors which is the reciprocal of resistance. Generally, it is denoted with the ‘G’ symbol and its unit is ‘Siemens’ denoted with the ‘S’ symbol.

#### Power in Resistors in Parallel

The power in resistors in parallel combination is similar to the series combination.

The whole power is equivalent to the amount of power dissolved through the individual resistors. Similar to series combination, the whole power utilized by the parallel combination is

**P _{T} = P_{1}+P_{2}+P_{3}+….Pn**

The simple method to measure power in watts which are dissolved through a resistor in the circuit is by using Joule’s law like **P = IV**

In the above equation, where electric power is ‘P’, voltage is ‘V’, and current ‘I’.

In this condition, the flow of current in every resistor is equal. By substituting V = IR (Ohm’s law) into Joule’s law, then we can get the power dissolved through the initial resistor as

**P1 = I^2R1**

**P2 = I^2R2**

**P3 = I^2R3**

### Resistors in Parallel Example Problems

**Example1**: In the following circuit, two resistors are connected in parallel which is R1 = 15Ω and R2 = 25Ω. So what is the total resistance for the below circuit?

We know that R1 = 15 Ω & R2 = 25 Ω

The total resistance RT = R1xR2/R1+R2

RT = 15×25/15+25 => 375/40 = 9.375 Ω

**Example2:** In the following parallel circuit, the resistor values like R1 = 10 Ω, R2 = 15Ω & R3=25Ω. Find the currents at individual branches & the whole current drawn from the power supply for the following set of resistors connected together in a parallel combination.

We know that R1 = 15 Ω, R2 = 25 Ω & R3 = 30Ω, Vs = 12V

The voltage supply is common to all three resistors in a parallel circuit. So Ohms Law is used to measure the current flow at every branch.

I1 = Vs/R1 = 12/15 = 0.8 Amps

I2 = Vs/R2 = 12/25 = 0.48 Amps

I3 = Vs/R3 = 12/30 = 0.4 Amps

The whole circuit current (IT) flowing through the resistors in parallel combination is;

I_{T} = I1+I2+I3 => 0.8+0.48+0.4 = 1.68 Amps

The value of total circuit current is 1.68 and the total resistance can be calculated as

1/R_{T } = 1/R1+1/R2+1/R3

1/R_{T } = 1/15+1/25+1/30 => 0.066+0.04+0.033

1/R_{T } = 0.139

R_{T } = 1/0.139 = 7.194 Ω

The total current flowing through the circuit is

I_{T} = V_{T}/R_{T }=> 12/7.194 => 1.66 Amps

### Advantages

The **advantages of resistors in parallel** include the following.

- When resistors are connected in parallel, then the voltage is stable. So the potential difference across every resistor is equivalent to the voltage supplied.
- We can add or remove a new resistor within the circuit without affecting other used components within the circuit.

### Disadvantages

The **disadvantages of resistors in parallel** include the following.

- Needs additional wires to connect in parallel combination.
- The voltage cannot be increased since the resistance reduces within the parallel circuit.
- This connection will not work once it requires flowing accurately a similar amount of current throughout the units.
- Its design is complicated and expensive as well.
- A short circuit may occur unexpectedly.
- If there is an error in one of the paths, then-current will supply throughout different circuit paths.

### What are parallel circuits used for?

The **applications of resistors in parallel** include the following.

- In every house, electrical wiring can be done in the Parallel Circuit form.
- The parallel circuits are used in dc power supply of the automobile industry.
- The computer hardware can be designed through this combination.

**What is the rule for resistance in parallel?**

In a parallel circuit, the whole resistance is always low as compared to any of the resistances branches. Once you add several branches to the parallel circuit, then the whole current will rise as Ohm’s Law states that when the resistance is low, then the current will be high.

**What is the resistance of two resistors in parallel?**

Once two resistors are connected in parallel, then equivalent resistance will be the product of resistors divided through their sum. When these resistors have a similar value, then equivalent parallel resistance is accurately half of the actual resistance.

**What is a parallel resistance?**

If the terminals of resistors are connected to the similar two nodes then it is known as parallel resistance. So, an equivalent resistance result is always less than each independent resistor.

Thus, this is all about an overview of parallel circuits, example problems, and their applications. The main function of these circuits is to maintain the flow of current in the parallel connection once one pathway is broken up. The best example is light fixtures because it uses several light bulbs. Once a bulb within the light fixture gets damaged then the light fixture maintains the flow of current in the remaining bulbs. Here is a question for you, what are resistors in series connection?