Question

how can three resistors of resistance 2ohm ,3ohm &6ohm be connected to give a total resistance of a)4ohm b)1 ohm?

Answer 1

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Answer 2

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