For the given mixed combination of resistors calculate the total resistance between points A and B.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 18\,\Omega \)
Reduce the network from the top of the triangle downwards, combining resistors in series (add) and in parallel (product over sum) at each level.
The two \( 4\,\Omega \) resistors at the apex are in series, and this branch is in parallel with the \( 8\,\Omega \) resistor:
\( 4 + 4 = 8\,\Omega \)
\( 8\,\Omega \parallel 8\,\Omega = 4\,\Omega \)
This \( 4\,\Omega \) is in series with the two side \( 4\,\Omega \) resistors, and the result is in parallel with the \( 12\,\Omega \) resistor:
\( 4 + 4 + 4 = 12\,\Omega \)
\( 12\,\Omega \parallel 12\,\Omega = 6\,\Omega \)
Finally the two \( 6\,\Omega \) resistors near A and B are in series with this \( 6\,\Omega \):
\( \displaystyle R_{AB} = 6 + 6 + 6 = 18\,\Omega \)