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Equivalent Resistance Formula

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Equivalent resistance is defined as the total resistance of the circuit for the resistors connected in series or parallel combination. Resistors are electrical devices that limit the current flow in a circuit and obey Ohm’s law, V = IR. A circuit may have more than one resistor present due to which equivalent resistance is evaluated accordingly. The value of current and voltage depends on the orientation of resistors in the circuit. 

In this article, we will learn about the Equivalent Resistance Formula in Series and Parallel combinations in detail.

What is the Equivalent Resistance?

Equivalent Resistance is the total resistance of the combination of all the resistances in the circuit. Suppose there are n resistance added in the circuit either in series or in parallel combination and if we replace all the resistance with a single resistance such that the current and the voltage difference in the circuit do not change it is called equivalent resistance.

Unit of Equivalent Resistance

Equivalent resistance is denoted by the symbol Req. SI unit of the measurement of Equivalent Resistance is Ohm (Ω) and the dimensional formula of the Equivalent Resistance [M1L2A−2T−3].

Formula for Equivalent Resistance

Equivalent Resistance is calculated using the Equivalent Resistance Formula, and the equivalent resistance formula is different in series and parallel combinations, i.e., we have two different equivalent resistance formulas they are,

  • Equivalent Resistance Formula for Series Combination.
  • Equivalent Resistance Formula for Parallel Combination.

Now, let’s learn about both formulas in detail in this article,

Equivalent Resistance Formula for Series Combination

In a series circuit of resistors, n resistors (n > 1) are connected adjacently one after the other, such that the collection of these resistors can be replaced by a single equivalent resistor to give the same resistance value. Here, the sum of the individual resistances will be the equivalent resistance of a series of resistors. The current through each resistor is the same but the voltage gets divided into n parts among the resistors.

Resistance Formula for Series Combination

 

Req = R1 + R2 + R3 + ….. + Rn

where,
Req is the equivalent resistance,
R1 is the resistance of the first resistor,
R2 is the resistance of the second resistor,
R3 is the resistance of the third resistor,
Rn is the resistance of the nth resistor,

Equivalent Resistance Formula for Parallel Combination

In a parallel circuit of resistors, n resistors (n > 1) are connected parallelly via wires that start from a common point. Here, the sum of the reciprocals of individual resistances equals the reciprocal of the equivalent resistance. The voltage through each resistor is the same but the current gets divided into n parts among the resistors.

Resistance Formula for Parallel Combination

 

1/Req = 1/R1 + 1/R2 + 1/R3 + ….. + 1/Rn

where,
Req is the equivalent resistance,
R1 is the resistance of the first resistor,
R2 is the resistance of the second resistor,
R3 is the resistance of the third resistor,
Rn is the resistance of the nth resistor,

How to find Equivalent Resistance?

The equivalent resistance of any circuit can easily be calculated using the steps given below,

Step 1: Study the electric circuit and mark all the resistance in the circuit along with the voltage of the battery.

Step 2: Check whether the resistance added is in series or parallel combination or both.

Step 3: Use the Equivalent Resistance Formula for Series Combination or Parallel combination accordingly.

Step 4: Simplify the formula in step 3 to get the Equivalent Resistance.

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Solved Examples on Equivalent Resistance Formula

Example 1: What is the equivalent resistance if three resistances of 4 Ω, 2 Ω, and 5 Ω are connected in series?

Solution:

We have,

R1 = 4 Ω
R2 = 2 Ω
R3 = 5 Ω

Using the formula we get,

Req = R1 + R2 + R3

      = 4 + 2 + 5

      = 11 Ω

Example 2: Find the unknown resistance if three resistances of 2 Ω, 5 Ω, and x Ω are connected in series to give an equivalent resistance of 10 Ω.

Solution:

We have,

R1 = 2 Ω
R2 = 5 Ω

Req = 10 Ω

Using the formula we get,

Req = R1 + R2 + R3

10 = 2 + 5 + x

10 = 7 + x

x = 3 Ω

Example 3: Find the unknown resistance if three resistances of 7 Ω, 3 Ω, and X Ω are connected in series to give an equivalent resistance of 15 Ω.

Solution:

We have,

R1 = 7 Ω
R2 = 3 Ω

Req = 15 Ω

Using the formula we get,

Req = R1 + R2 + R3

15 = 7 + 3 + X

15 = 10 + 

x = 5 Ω

Example 4: What is the equivalent resistance if three resistances of 6 Ω, 3 Ω, and 8 Ω are connected in parallel?

Solution:

We have,

R1 = 6 Ω
R2 = 3 Ω
R3 = 8 Ω

Using the formula we get,

1/Req = 1/R1 + 1/R2 + 1/R3

1/Req = 1/6 + 1/3 + 1/8

1/Req = (4+8+3)/24

1/Req = 15/24

Req = 24/15 Ω = 1.6 Ω

Example 5: Find the unknown resistance if three known resistances of 4 Ω, 2 Ω, and 1 Ω connected in series with an unknown resistance of X Ω give an equivalent resistance of 0.5 Ω.

Solution:

We have,

R1 = 4 Ω
R2 = 2 Ω
R3 = 1 Ω

Req = 0.5 Ω 

Using the formula we get,

1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4 

1/0.5 = 1/4 + 1/2 + 1/1 + 1/R4 

1/R4 = 1/4 + 1/2 + 1/1 – 1/0.5

1/R4 = 1/4

R4 = 4 Ω

FAQs on Equivalent Resistance Formula

Question 1: What is the “equivalent resistance” formula in the Series combination?

Answer:

The “equivalent resistance” formula in the Series combination is given below,

Req = R1 + R2 + R3 + ….. + Rn

Question 2: What is the condition for the series combination of resistance?

Answer:

For the resistor to be connected in series combination the important conditions are,

  • The current passing through each resistor is the must be same.
  • The resistors are connected in a linear manner.

Question 3: What is the “equivalent resistance” formula in the Parallel combination?

Answer:

The “equivalent resistance” formula in the Parallel combination is given below,

1/Req = 1/R1 + 1/R2 + 1/R3 + ….. + 1/Rn

Question 4: What is the condition for the parallel combination of resistance?

Answer:

For the resistor to be connected in parallel combination the important conditions are,

  • The voltage difference across each resistor is the same.
  • The resistors are connected parallel to each other.


Last Updated : 04 Feb, 2024
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