Question

if 2 ohm, 3 ohm and 5 ohm are connected in parallel, will the value of total resistance be less than 2 ohm or greater than 5 ohm or lie between 2 ohm and 5 ohm? explain.

Answer 1

1/r=1/r1+1/r2+1/r3
1/r=1/2+1/3+1/5
1/r=(15+10+6)/30=31/30
thus total resistance=31/30=0.96
r(total)<2 ohm

Answer 2

analytical method : a/c to question,

    2Ω, 3Ω and 5Ω are connected in parallel combination.

we know, if R₁ , R₂ , R₄ ....... Rₙ are connected in parallel combination then, equivalent resistance, $R_{eq}$ is given as ....

1/Req = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ + ...... + 1/Rₙ

so, total or, equivalent resistance of given resistances, 1/ Req = 1/2Ω + 1/3Ω + 1/5Ω

= (15 + 10 + 6)/(30Ω)

= 31/(30Ω)

hence, $R_{eq}$ = 30Ω/31 ≈ 0.9677Ω < 2Ω

hence, total resistance of 2Ω, 3Ω and 5Ω will be less than 2Ω.

logical method : in parallel combination, equivalent or, total or, resultant resistance is less than the least resistance connected in the circuit.

here there are three resistors of resistance ; 2Ω, 3Ω and 5Ω.

it is clear that, 2Ω is the least resistance.

so, total resistance must be less than 2Ω.

hence, total resistance will be less than 2Ω