[tex]\star\:{\underline{\underline{\sf{\purple{ \: Question \: 19\: }}}}} [/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given \: :}}}}}}[/tex]
☆ Number of resistors = 5
☆ Resistance of each resistors = [tex]\tt \dfrac{1}{5} \text{\O}mega[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find \: :}}}}}}[/tex]
☆ Maximum resistance which can be made.
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution \: :}}}}}}[/tex]
• To get maximum resistance, connect the all the given resistances in series.
For,
Series combination :-
[tex] \longrightarrow \sf R_{s} = R_{1} + R_{2} + R_{3} + R_{4} + R_{5} [/tex]
[tex] \longrightarrow \sf R_{s}= \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} [/tex]
[tex] \longrightarrow \sf R_{s} = \dfrac{1 + 1 + 1 + 1 + 1}{5} [/tex]
[tex]\longrightarrow \sf R_{s} = \cancel{ \dfrac{5}{5} }[/tex]
[tex] \longrightarrow \sf R_{s} = \purple{1 \: \text{\O}mega}[/tex]
[tex] \therefore[/tex] Maximum resistance is 1 Ω.
[tex] \star\:{\underline{\underline{\sf{\red{ \: Question \: 20\: }}}}} [/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given \: :}}}}}}[/tex]
☆ Number of resistors = 5
☆ Resistance of each resistors = [tex]\tt \dfrac{1}{5} \text{\O}mega[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find \: :}}}}}}[/tex]
☆ Minimum resistance which can be made.
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution \: :}}}}}}[/tex]
• To get minimum resistance, connect the all the given resistances in parallels.
For,
Parallel combination :-
[tex] \longrightarrow \sf \dfrac{1}{R_{p}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+\dfrac{1}{R_4}+\dfrac{1}{R_5}[/tex]
[tex] \longrightarrow \sf\dfrac{1}{R_{p}}= \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } [/tex]
[tex] \longrightarrow \sf\dfrac{1}{R_{p}}= 1 \times \dfrac{5}{1} +1 \times \dfrac{5}{1} +1 \times \dfrac{5}{1} + 1 \times \dfrac{5}{1} + 1 \times \dfrac{5}{1}[/tex]
[tex]\longrightarrow \sf\dfrac{1}{R_{p}}= \dfrac{5}{1} + \dfrac{5}{1} + \dfrac{5}{1} + \dfrac{5}{1} + \dfrac{5}{1}[/tex]
[tex]\longrightarrow \sf\dfrac{1}{R_{p}}= 25[/tex]
[tex]\longrightarrow \sf R_{p}= \red{ \dfrac{1}{25} \: \text{\O}mega}[/tex]
[tex] \therefore[/tex] Minimum resistance is [tex]\dfrac{1}{25} [/tex] Ω.
[tex] {\large{\textsf{\textbf{\underline{\underline{Note \: :}}}}}}[/tex]
☆ Figure in attachment.
[tex]{\underline{\rule{290pt}{2pt}}}[/tex]
