Question

The equivalent resistance between A and B in the figure is:

• A. $5\Omega$
• B. $3\Omega$
• C. $8\Omega$
• D. $4\Omega$

Answer 1

Answer: (B)

$3\Omega$

In this case, the 2 resistors of 3 ohms and 2 ohms on the upper half of the circuit are connected in series and the combined resistance R1 is given as 3+2 = 5 ohms.
The 2 resistors of 6 ohms and 4 ohms on the lower half of the circuit are connected in series and the combined resistance R2 is given as 6+4 = 10 ohms.
The resistances R1, R2 and 30 ohms in the middle are connected in parallel. So the total resistance R of this parallel connection is given as $\frac{1}{5}+\frac{1}{10}+\frac{1}{30}=\frac{1}{0.33}=3ohms$. That is, the resistance in the closed loop is reduced to 3 ohms.
Hence, the value of the resistance in the circuit between A and B is 3 ohms.