Question

Three resistors of 1 Ω, 2 ft and 3 Ω are connected in parallel. The combined resistance of the three resistors should be
(a) greater than 3 Ω
(b) less than 1 Ω
(c) equal to 2 Ω
(d) between 1 Ω and 3 Ω

Answer 1

Answer:

May right answer is less than 1ohm

Answer 2

Answer:

The correct answer is option (b) less than 1 Ω.

Explanation:

Step 1: For parallel resistors,

$\frac{1}{Rp} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3}$

Step 2: If R1 = 1 Ω, R2 = 2 Ω and R3 = 3 Ω then,

$\frac{1}{Rp} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3}$

$= 1 + \frac{1}{2} + \frac{1}{3}$

$= 1 + \frac{3 + 2}{6}$

$= 1 + \frac{5}{6}$

$= \frac{6 + 5}{6}$

So,

$\frac{1}{Rp} = \frac{11}{6}$

So, Rp = 6 / 11

= 0.54 Ω

Which is less than 1Ω.

So, the combined resistance of 3 parallel resistance 1Ω, 2Ω and 3Ω should be less than 1Ω.

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