Question

The effective resistance between the points A and B in the circuit shown in Fig. will be :

• A. $6\Omega$
• B. $3\Omega$
• C. $15\Omega$
• D. $10\Omega$

Answer 1

The correct option is B $3\Omega$

In this case, the $3$ resistors of $1\Omega$ on the upper half of the circuit are connected in series and the combined resistance $R_1$ is given as $1+1+1=3\Omega$ .
The 3 resistors of $2$ ohms on the lower half of the circuit are connected in series and the combined resistance $R_2$ is given as $2+2+2=6\Omega$.
The resistances $R_1$ , $R_2$ and $2\Omega$ in the middle are connected in parallel. So the combined resistance R3 of this parallel connection is given as $\frac{1}{3}+\frac{1}{2}+\frac{1}{6}=\frac{1}{1}=1ohm$. That is, the resistance in the closed loop is reduced to 1 ohm.
Now the total resistance $R$ across the circuit is given as $R_1+R_2+R_3=1+1+1=3\Omega$.
Hence, the value of the resistance in the circuit from A to B is $3\Omega$.