Question

In the arrangement of resistances shown below. The effective resistance between points A and B is

• A. $20\Omega$
• B. $30\Omega$
• C. $90\Omega$
• D. $110\Omega$

Answer 1

Answer: (A)

$20\Omega$

Due to resistances being symmetrically double at the bottom half of the circuit, the current distributes symmetrically such that the current in upper resistances is double of that of lower resistances.

The distribution has been shown in figure above.

Applying Kirchoff's Current Law ,

$2i_1=x+(2i_1-2i_2)$

Also, $i_1=x+(i_1-i_2)$

Solving the above equations gives,

$x=0$

Hence the vertical resistances can be neglected.
The equivalent resistance of the upper branch $=$$5\Omega +10\Omega +15\Omega =30\Omega$

Similarly for lower branch, equivalent resistance$=$$10\Omega +20\Omega +30\Omega =60\Omega$

These resistances are in parallel. Hence the total equivalent resistance is $20\Omega$