Question

In the circuit diagram shown each resistance is of value $1$ ohm, what is the equivalent resistance between the points A and B?

• A. $4/7\Omega$
• B. $8/7\Omega$
• C. $3/14\Omega$
• D. $16/7\Omega$

Answer 1

The correct option is B $8/7\Omega$

By symmetry,

Current in arm $CE=$ Current in arm $ED$. The resistance of the network will not be affected if the wire $CED$ is disconnected from the wire $AED$ at the point $E$, as shown in below figure.

$\to R_4$ and $R_5$ in series $⟹R_{45}=2\Omega$

$R_{45}$ is in parallel with $R_2⟹R_{452}=\frac{2\times 1}{2+1}=\frac{2}{3}\Omega$

$\to R_1,R_{452}$ and $R_3$ in series $⟹1+\frac{2}{3}+1=\frac{8}{3}\Omega \to \left(1\right)$

$R_6$ and $R_8$ in series $⟹2\Omega \to \left(2\right)$

$\left(1\right)$ and $\left(2\right)$ are in parallel connection.

$⟹$ The resusltant resistance,

$\frac{1}{Req}=\frac{3}{8}+\frac{1}{2}=\frac{3+4}{8}=\frac{7}{8}$

$⟹Req=\frac{8}{7}\Omega$ is the correct answer.