Question

The given figure shows a network of resistances. The effective resistance between points $A$ and $B$ of network is

• A. $(3/2)\Omega$
• B. $6\Omega$
• C. $3\Omega$
• D. $2\Omega$

Answer 1

Answer: (D)

Resistance of arm $AFE=3+3=6\Omega$
The arms $AFE$ and $AE$ are in parallel, their effective resistance
$=\frac{6\times 6}{6+6}=3\Omega$
Resistance of arm $AED=3+3=6\Omega$
Effective resistance between $A$ and $D$ of portion $AFED$
$=\frac{6\times 6}{6+6}=3\Omega$
Effective resistance between $A$ and $C$ of portion
$AFEDC=\frac{(3+3)\times 6}{(3+3)+6}=3\Omega$
Resistance of arm $AFEDCB=3+3=6\Omega$
For resistance between $A$ and $B,6\Omega$ and $3\Omega$ are in parallel.
Thus effective resistance, $R_P=\frac{3\times 6}{3+6}=2\Omega$