Three resistors of 1 Ω, 2Ω and 3 Ω are connected in parallel. The combined resistance of the three resistors will be
Select one:
a. Less than 1 Ω
b. Greater than 3 Ω
c. Equal to 2 Ω
d. Between 1 Ω and 3 Ω Correct
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Three resistors of 1 Ω, 2Ω and 3 Ω are connected in parallel. The combined resistance of the three resistors will be
Select one:
a. Less than 1 Ω
b. Greater than 3 Ω
c. Equal to 2 Ω
d. Between 1 Ω and 3 Ω Correct
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Answer:
a. Less than 1Ω
Explanation:
Equivalent resistance (R) of these 3 resistors can be calculated as:
1 / R = 1 / 1 + 1 / 2 + 1 / 3 = 11 / 6
⇒ R = 6 /11
We can clearly observe that 6 / 11 is lesser than 1.
Hence, option (a) is the correct answer.
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Given :
R₁ = 1 ohm
R₂ = 2 ohm
R₃ = 3 ohm
To Find :
The combined resistance of the three resistors
Solution :
Given, the resistors are connected in parallel combination.
We are required to find the equivalent resistance of the three resistors connected in parallel.
Let the equivalent resistance be 'R'
∴ [tex]\frac{1}{R}[/tex] = [tex]\frac{1}{1}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{3}[/tex]
⇒ [tex]\frac{1}{R}[/tex] = [tex]\frac{6 + 3 + 2}{6}[/tex]
⇒ [tex]\frac{1}{R}[/tex] = [tex]\frac{11}{6}[/tex]
∴ R = [tex]\frac{6}{11}[/tex] = 0.545 ohm
Hence, the equivalent resistance (R) is 0.545 ohm.
As R < 1Ω ,
Thus, Option (a) is correct.