Question

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Answer 1

$\star\:{\underline{\underline{\sf{\purple{ \: Question \: 19\: }}}}}$

${\large{\textsf{\textbf{\underline{\underline{Given \: :}}}}}}$

☆ Number of resistors = 5

☆ Resistance of each resistors = $\tt \dfrac{1}{5} \text{\O}mega$

${\large{\textsf{\textbf{\underline{\underline{To \: Find \: :}}}}}}$

☆ Maximum resistance which can be made.

${\large{\textsf{\textbf{\underline{\underline{Solution \: :}}}}}}$

• To get maximum resistance, connect the all the given resistances in series.

For,

Series combination :-

$\longrightarrow \sf R_{s} = R_{1} + R_{2} + R_{3} + R_{4} + R_{5}$

$\longrightarrow \sf R_{s}= \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5}$

$\longrightarrow \sf R_{s} = \dfrac{1 + 1 + 1 + 1 + 1}{5}$

$\longrightarrow \sf R_{s} = \cancel{ \dfrac{5}{5} }$

$\longrightarrow \sf R_{s} = \purple{1 \: \text{\O}mega}$

$\therefore$ Maximum resistance is 1 Ω.

$\star\:{\underline{\underline{\sf{\red{ \: Question \: 20\: }}}}}$

${\large{\textsf{\textbf{\underline{\underline{Given \: :}}}}}}$

☆ Number of resistors = 5

☆ Resistance of each resistors = $\tt \dfrac{1}{5} \text{\O}mega$

${\large{\textsf{\textbf{\underline{\underline{To \: Find \: :}}}}}}$

☆ Minimum resistance which can be made.

${\large{\textsf{\textbf{\underline{\underline{Solution \: :}}}}}}$

• To get minimum resistance, connect the all the given resistances in parallels.

For,

Parallel combination :-

$\longrightarrow \sf \dfrac{1}{R_{p}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+\dfrac{1}{R_4}+\dfrac{1}{R_5}$

$\longrightarrow \sf\dfrac{1}{R_{p}}= \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} } + \dfrac{1}{ \frac{1}{5} }$

$\longrightarrow \sf\dfrac{1}{R_{p}}= 1 \times \dfrac{5}{1} +1 \times \dfrac{5}{1} +1 \times \dfrac{5}{1} + 1 \times \dfrac{5}{1} + 1 \times \dfrac{5}{1}$

$\longrightarrow \sf\dfrac{1}{R_{p}}= \dfrac{5}{1} + \dfrac{5}{1} + \dfrac{5}{1} + \dfrac{5}{1} + \dfrac{5}{1}$

$\longrightarrow \sf\dfrac{1}{R_{p}}= 25$

$\longrightarrow \sf R_{p}= \red{ \dfrac{1}{25} \: \text{\O}mega}$

$\therefore$ Minimum resistance is $\dfrac{1}{25}$ Ω.

${\large{\textsf{\textbf{\underline{\underline{Note \: :}}}}}}$

☆ Figure in attachment.

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