Total Resistance in a Parallel Circuit
Last Updated :
23 Jul, 2025
The opposition to the current flowing in a circuit is called resistance. In other words, resistance is the measurement of opposition of current in a circuit. The SI unit of resistance is Ohm (Ω). Commonly it is denoted as R.
According to Ohm's law, resistance is ratio of voltage applied to current flowing in a circuit. Formula on the basis of Ohm's law is:
V = IR
where,
V is applied voltage,
I is current, and
R is resistance of given circuit.
Resistance is a crucial property in various electrical devices and systems, including resistors in circuits, heating elements in appliances, and thermistors in temperature sensors. Understanding and controlling resistance is essential in designing and maintaining efficient and safe electrical systems.
What is a Parallel Circuit
A parallel circuit is a circuit in which all the components are connected parallelly with the same point of contact. In a parallel circuit, the components are connected equidistant with each other. The voltage in a parallel circuit is the same for all the components whereas the current flowing through the parallel circuit is variable for all the components. The total resistance can be calculated by adding the reciprocals of all the connected resistances and taking the reciprocal of the resultant value.
One key characteristic of a parallel circuit is that the voltage across each component remains the same. This is because all components are connected directly across the voltage source, so they experience the same potential difference. Therefore, regardless of the number or type of components in the circuit, the voltage remains constant.
Parallel Resistor Circuit
In a parallel circuit the voltage is same for all the resistors connected in parallel but the current flowing through the circuit is different for all the resistors. The total resistance in a parallel circuit is calculated by taking the reciprocal of the sum of the reciprocals of all the resistances connected in parallel.
CircuitIn the above diagram resistors R1, R2 and R3 are connected in parallel, and the voltage V Volts is applied on the circuit. A current 'I' is flowing through the parallel circuit. We know that the voltage in parallel circuit is same for all the resistors so, the same voltage is applied across the resistors R1, R2 and R3 whereas the current is divided among all the resistors R1, R2 and R3. The current flowing through R1, R2 and R3 be I1, I2 and I3 respectively. The total current flowing through the circuit is the sum of individual current flowing through each component.
The following formulas are used to find total resistance in a parallel circuit. Let V be the applied voltage on the parallel circuit with resistors R1, R2 and R3 with total current 'I' flow through the circuit. As we know in the parallel circuit the current is different for all the components so, the current flowing through R1, R2 and R3 is I1, I2 and I3 respectively.
According to Ohm's Law,
I = V / R
We know that the current I is divided among resistors R1, R2 and R3 as I1, I2 and I3 and voltage V is same. Therefore,
I = V/R
I1 = V/R1
I2 = V/R2
I3 = V/ R3
and
I = I1 + I2 + I3
Putting the values of I, I1, I2 and I3
V/R = V/R1 + V/R2 + V/R3
V/R = V × [1/R1 + 1/R2 + 1/R3]
1/R = [1/R1 + 1/R2 + 1/R3]
1/R = [1/R1 + 1/R2 + 1/R3]
or
R = (R1 × R2 × R3) / (R1 R2+ R2R3 + R3R1)
where,
R1 is resistance of resistor R1
R2 is resistance of resistor R2
R3 is resistance of resistor R3
So, the total resistance in a parallel circuit is equal to the product of all the resistances connected in parallel divided by the sum of all the resistances in parallel.
Generalized Formula to Calculate Total Resistance in Parallel Circuit
Let R1, R2, ...., Rn resistors are connected in parallel circuit. So, the total resistance of this circuit can be calculated by:
1/R = [1/R1 + 1/R2 + ... + 1/Rn]
Various Parallel Resistor Networks
Given Below are the various circuit representation of the parallel resistor Networks
Various Parallel Resistor NetworksIn the given three connections, regardless of how the resistors are physically positioned or interconnected, they share the same electrical characteristics because they are connected in parallel.
Solved Examples on Parallel Circuit
Find the total resistance of a parallel circuit in which resistances of resistors R1, R2 and R3 are 10Ω, 15Ω and 20Ω respectively.
Parallel Circuit with three resistorsThe total resistance of parallel circuit is calculated by the formula:
R = (R1 × R2 × R3) / (R1 R2+ R2R3 + R3R1)
R = (10 × 15 × 20) / (300 + 150 + 200)
R = 3000 / 650
R = 4.6153 Ω
Total resistance of given parallel circuit is 4.6153 Ω.
Find the resistance of resistor R1 if the resistance of R2 is given as 18Ω and total resistance of the parallel circuit is given as 15Ω.
The total resistance of parallel circuit is calculated by the formula:
1/R = [1/R1 + 1/R2]
1/15 = [1/R1 + 1/18]
1/R1 = 1/15 - 1/18
1/R1 = 3 / (15 × 18)
R1 = 90 Ω
The resistance of resistor R1 is 90 Ω.
Advantages of Parallel Circuit
Below are some advantages of parallel circuit:
- The voltage across each component is same.
- The installation of new components is easy.
- If one component fails, it does not affect the entire circuit.
Disadvantages of Parallel Circuit
Below are some disadvantages of parallel circuit:
- Parallel circuit includes lots of wiring.
- If all the components require same current then, parallel circuits fail to do this.
Applications of Parallel Circuit
There are multiple applications of parallel circuit. Some of these applications of parallel circuits are as follows:
- It is used in household outlets to provide same voltage.
- It is used in factory for different equipment so that if one fails it will not affect the entire work.
- It is used in automobile headlights.
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