Find the equivalent resistance across the two ends $A$ and $B$ of this circuit.
Find the equivalent resistance across the two ends $A$ and $B$ of this circuit.
From the diagram, we find that the following pairs of resistors are.in parallel.
$R _{1}$ and $R _{2}, R _{3}$ and $R _{4}, R _{5}$ and $R _{6},$ and $R _{7}$ and $R _{8}$.
Therefore, we have
$\frac{1}{ R _{12}}=\frac{1}{ R _{1}}+\frac{1}{ R _{2}}=\frac{1}{2}+\frac{1}{2}=1 ohm$
or $R _{12}=1 ohm$
Similarly, $R _{34}=1 ohm , R _{56}=1 ohm$ and $R _{78}=1 ohm$
Now, $R _{12}$ and $R _{34}$ are in series, therefore,
$R _{1234}=1+1=2 ohm$
Also, $R _{56}$ and $R _{78}$ are in series, therefore,
we have $R _{5678}=1+1=2 ohm$
Now, $R _{1234}$ and $R _{5678}$ are in parallel, hence, net resistance of the circuit is
$\frac{1}{ R }=\frac{1}{ R _{1234}}+\frac{1}{ R _{5678}}=\frac{1}{2}+\frac{1}{2}=1$
Hence, equivalent resistance $=1\,ohm.$
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