Resistors in Parallel Formula

Resistors in parallel formula

When resistors are used in electronic circuits, they can be used in different configurations. By determining the way of organizing the resistors we can calculate the resistance for the circuit or some portion of the circuit.

When two or more resistors are connected parallelly to each other in a circuit such that both terminals of one resistor are linked to each terminal of the other resistor or resistors are called resistors in parallel. A parallel circuit has another name called a current divider. It can allow the current of the circuit in a parallel resistor network to travel more than one channel since there are several pathways for it as. Hence, the current along all of the parallel network’s branches is not the same. The voltage drops across all resistors in a parallel resistive network, on the other hand, is constant.

By calculating the equivalent resistance of the circuit, we can get the total resistance of a parallel circuit. The reciprocal of the equivalent resistance equals the sum of the reciprocals of individual resistances connected in parallel is what the formula represents.

The symbol Req is used to denote the equivalent resistance. 

The SI unit of measurement is the ohm (Ω) 

 the dimensional formula is given = [M¹L²A^-2T^-3].

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + …… + 1/R_n

where,

R_eq means equivalent resistance,

R₁ means the resistance of the first resistor,

R₂ means the resistance of the second resistor,

R₃ means the resistance of the third resistor and so on.

Examples of Resistors in parallel formula

1) When three resistances of 5 Ω, 2 Ω and 7 Ω are parallelly connected then calculate the equivalent resistance.

Solution:

We have,

R₁ = 5 Ω

R₂ = 2 Ω

R₃ = 7 Ω

By applying the formula, we will get,

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

1/R_eq = 1/5 + 1/2 + 1/7

1/R_eq= 1/1.2

R_eq = 1.2 Ω

2)  If the given three resistances of 2 Ω, 1 Ω and 3 Ω are connected in parallel, then find the equivalent resistance.

Solution:

Given

R₁ = 2 Ω

R₂ = 1 Ω

R₃ = 3 Ω

By applying the formula, we will get,

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

= 1/2 + 1/1 + 1/3

 = 1/0.55

R_eq = 0.55 Ω

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