Determine the equivalent (total) resistance of the circuit if 3 resistors are connected in parallel and their individual resistance are 2Ω, 1.5Ω and 4Ω respectively.
Question
Determine the equivalent (total) resistance of the circuit if 3 resistors are connected in parallel and their individual resistance are 2Ω, 1.5Ω and 4Ω respectively.
Solution
To find the equivalent resistance (Re) of resistors connected in parallel, we use the formula:
1/Re = 1/R1 + 1/R2 + 1/R3
Where R1, R2, and R3 are the resistances of the individual resistors.
Step 1: Substitute the given values into the formula:
1/Re = 1/2Ω + 1/1.5Ω + 1/4Ω
Step 2: Calculate the reciprocals:
1/Re = 0.5 + 0.6667 + 0.25
Step 3: Add the values:
1/Re = 1.4167
Step 4: To find Re, take the reciprocal of the result:
Re = 1 / 1.4167
Re = 0.706 Ω
So, the equivalent resistance of the circuit is approximately 0.706 Ω.
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