Question

Three resistors of 2 ohm 3
ohm and 6ohm are give what is the least resistance that you can get using all of them​

Answer 1

GiveN :

Three resistors are given with magnitude as $\sf{2 \Omega \: , \: 3 \Omega \: and \: 6 \Omega}$ respectively.

To FinD :

Least value of the three resistances.

SolutioN :

For the maximum value of the resistances we've to connect all of them in the $\tt{\green{Series \: combination}}$ , where as for calculating the minimum value of the resistance we've to connect then in $\tt{\green{Parallel \: combination}}$ .

Let,

$\rm{R_1 = 2 \Omega}$

$\rm{R_2 = 3 \Omega}$

$\rm{R_3 = 6 \Omega}$

Add them in parallel for getting minimum value :

$\implies \rm{\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}} \\ \\ \\ \implies \rm{\dfrac{1}{R_{eq}} = \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{6}} \\ \\ \\ \implies \rm{\dfrac{1}{R_{eq}} = \dfrac{3 + 2 + 1}{6}} \\ \\ \\ \implies \rm{\dfrac{1}{R_{eq}} = \dfrac{6}{6}} \\ \\ \\ \implies \rm{\dfrac{1}{R_{eq}} = 1} \\ \\ \\ \large \implies {\boxed{\rm{R_{eq} = 1 \Omega}}}$

Answer 2

"$\bf{ \pmb{ \underline{\gray{GIVEN}}}} \\ \sf \: \small{ Three \: resistors \: of \: 2 Ω, 3 Ω \: and \: 6 Ω \: are \: given \: respectively. }\\ \\ \\ \bf{ \pmb{ \underline{\gray{TO \: FIND }}}}\\ \rm \small{Least \: value \: of \: the \: three \: resistances. }\\ \\ \\ \bf { \pmb{ \underline{\gray{ SOLUTION}}}} \\ \tt \tiny{For \: the \: max \: value \: of \: the \: resistances, resistor \: are \: connected \: in \: \bf{\blue{Series \: Combination}} }\\ \tt \tiny{For \: the \: least \ value\ of \: the \: resistances, resistor \: are \: connected \: in\ \bf{\green{Parallel \: Combination}} } \\ \\ \cal \: \small{\red{Connect \: the \: resistor \: in \: parallel \: for \: getting \: least \: value :} }\\ \\ \begin{gathered}\small \rm{\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}} \\ \\ \small \rm{\dfrac{1}{R_{eq}} = \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{6}} \\ \\ \\ \small \rm{\dfrac{1}{R_{eq}} = \dfrac{3 + 2 + 1}{6}} \\ \\ \small \rm{\dfrac{1}{R_{eq}} = \dfrac{6}{6}} \\ \\ \small \rm{\dfrac{1}{R_{eq}} = 1} \\\\ \large { \boxed{\bf \blue{R_{eq} = 1 Ω}}}\end{gathered}$