$(a)$ What is the total resistance of $n$ resistors each of resistance ' $R^{\prime}$ connected in
$(i)$ series ?
$(ii)$ parallel ?
$(b)$ Calculate the resultant resistance of $3$ resistors $3\, \Omega, 4\, \Omega$ and $12\, \Omega$ connected in parallel.
$(a)$ What is the total resistance of $n$ resistors each of resistance ' $R^{\prime}$ connected in
$(i)$ series ?
$(ii)$ parallel ?
$(b)$ Calculate the resultant resistance of $3$ resistors $3\, \Omega, 4\, \Omega$ and $12\, \Omega$ connected in parallel.
$(a)$ In series combination, we have
$R_{S}=R_{1}+R_{2}+\ldots$ to $n=n R$
In parallel combination, we have
$\frac{1}{ R _{ P }}=\frac{1}{ R _{1}}+\frac{1}{ R _{2}}+\ldots n$
Or $R _{ P }= R / n$
$(b)$ In parallel, we have
$\frac{1}{ R _{ P }}=\frac{1}{ R _{1}}+\frac{1}{ R _{2}}+\frac{1}{ R _{3}}=\frac{1}{3}+\frac{1}{4}+\frac{1}{12}$
or $\quad R_{P}=12 / 8=1.5 \Omega$
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