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Resistors in Parallel Formula

Resistors offer a resistance to the flow of current in a circuit The effective resistance depends on connection; whether it is connected in series or parallel. In series connection, the current will be constant whereas in parallel connection voltage will be constant through the circuit. So in household appliances, parallel connection is preferred. The formula for resistors in parallel connection is,
 Resistors in Parallel Formula

Where R1, R2,….,Rn are the resistors connected in parallel

 

Resistors in Parallel Problems

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Let us discuss the solved problems of resisters in parallel connection.

Solved Examples

Question 1: Calculate the resultant resistance of a parallel circuit containing three resistors; R1 = 2Ω, R2 = 4Ω and R3 = 6Ω?
Solution:

 
Given value of resistors are,
R1 = 2Ω, R2 = 4Ω, R3 = 6Ω
Formula for resistors in parallel is,

$\frac{1}{R_{p}}$ = $\frac{1}{R_{1}}$+$\frac{1}{R_{2}}$+….+$\frac{1}{R_{n}}$

$\frac{1}{R_{p}}$ = $\frac{1}{2}$+$\frac{1}{4}$+$\frac{1}{6}$

$\frac{1}{R_{p}}$ = 0.9166
So, $R_{p}$ = 1.0909Ω
 

Question 2: Calculate total resistance of the given parallel connection; R1 = 4Ω and R2 = 5Ω?
Solution:

 
Given value of resistors are,
R1 = 4Ω, R2 = 5Ω
Formula for resistors in parallel is,

$\frac{1}{R_{p}}$ = $\frac{1}{R_{1}}$+$\frac{1}{R_{2}}$+….+$\frac{1}{R_{n}}$

$\frac{1}{R_{p}}$ = $\frac{1}{4}$+$\frac{1}{5}$

$\frac{1}{R_{p}}$ = 0.45
So, $R_{p}$ = 2.222Ω

 

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