Question

Three resistor of 2ohm,3ohm and 6ohm are given in the class
1:What is the highest resistance that you can get using all of them?
2: What is the least resistance that you can get using all of them
3:Can you make a resistance 4.5ohm using these three? Draw the circuit​

Answer 1

Answer:

1. 2+3+6 = 11 ohm all in series

2. 1/ ( 1/2+1/3+1/6) = 6/5= 1.2 ohm all in parallel

3. 2,6 is parallel is 1/(1/2+1/6)= 1.5 with 3 is series is 4.5 ohm

Answer 2

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