Question

Equivalent resistance between point A and B in the combination of resistance shown is

• A. $7/5\Omega$
• B. $13/5\Omega$
• C. $9/8\Omega$
• D. $7/13\Omega$

Answer 1

The correct option is A $7/5\Omega$

If we reverse the potential in the circuit, the current in the branches must be same. Hence the current in the $1\Omega$ and $2\Omega$ resistances would be same, as shown in figure above.

Applying Kirchoff's voltage law in first smaller loop,

$-\left(i_1\right)\left(1\right)-(i_1-i_2)\left(1\right)+\left(i_2\right)\left(2\right)$

$⟹i_1=\frac{3i_2}{2}$

Hence $V_{AB}=(i_1+i_2)R_{eq}=\left(i_1\right)\left(1\right)+\left(i_2\right)\left(2\right)$

$⟹2.5i_2{R}_{eq}=3.5i_2$

$⟹R_{eq}=\frac{7}{5}\Omega$