Question
Explain the parallel connection of series resistors.
✓
Answer
(i) Let $R_1$ and $R_2$ be connected in parallel to give an effective resistance of $R_{P 1}$.
(ii) If you consider a connection of a set of series resistors connected in a parallel circuit, we get a parallel-series circuit.
(iii) Let $R_1$ and $R_2$ be connected in series to give an effective resistance of $R_{S 1}$.
(iv) Similarly, let $R_3$ and $R_4$ be connected in series to give an effective resistance of $R_{S 2}$.
(v) Then, both of these serial segments are connected in parallel.
Parallel - Series combination of resistors
Using equation $R_S=R_1+R_2+R_3$ we get
$R_S=R_1+R_2+R_3$
$R_{S 1}=R_1+R_2$
$R_{S 2}=R_3+R_4$
Finally, using equation, $\frac{1}{ R _{ p }}=\frac{1}{ R _1}+\frac{1}{ R _2}+\frac{1}{ R _3}$ the net effective resistance is given by
$\frac{1}{ R _{\text {total }}}=\frac{1}{ R _{ s 1}}+\frac{1}{ R _{ s 2}} .$
(ii) If you consider a connection of a set of series resistors connected in a parallel circuit, we get a parallel-series circuit.
(iii) Let $R_1$ and $R_2$ be connected in series to give an effective resistance of $R_{S 1}$.
(iv) Similarly, let $R_3$ and $R_4$ be connected in series to give an effective resistance of $R_{S 2}$.
(v) Then, both of these serial segments are connected in parallel.
Parallel - Series combination of resistors
Using equation $R_S=R_1+R_2+R_3$ we get
$R_S=R_1+R_2+R_3$
$R_{S 1}=R_1+R_2$
$R_{S 2}=R_3+R_4$
Finally, using equation, $\frac{1}{ R _{ p }}=\frac{1}{ R _1}+\frac{1}{ R _2}+\frac{1}{ R _3}$ the net effective resistance is given by
$\frac{1}{ R _{\text {total }}}=\frac{1}{ R _{ s 1}}+\frac{1}{ R _{ s 2}} .$
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