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Q. The given figure shows a network of resistances. The effective resistance between points $A$ and $B$ of network isPhysics Question Image

Current Electricity

Solution:

Resistance of arm $A F E=3+3=6\, \Omega$
The arms $A F E$ and $A E$ are in parallel, their effective resistance
$=\frac{6 \times 6}{6+6}=3\, \Omega$
Resistance of arm $A E D=3+3=6\, \Omega$
Effective resistance between $A$ and $D$ of portion $A F E D$
$=\frac{6 \times 6}{6+6}=3\, \Omega$
Effective resistance between $A$ and $C$ of portion
$A F E D C=\frac{(3+3) \times 6}{(3+3)+6}=3\, \Omega$
Resistance of arm $A F E D C B=3+3=6\, \Omega$
For resistance between $A$ and $B, 6\, \Omega$ and $3\, \Omega$ are in parallel.
Thus effective resistance, $R_{P}=\frac{3 \times 6}{3+6}=2\, \Omega$