Question

What is the equivalent resistance of the network shown in figure?

• A. $8\Omega$
• B. $\frac{16}{3}\Omega$
• C. $4\Omega$
• D. $\frac{16}{5}\Omega$

Answer 1

Answer: (B)

The network consists of four loops connected in series. Each loop consists of two $1\Omega$ resistors in series connected in parallel with two $2\Omega$ resistors in series. Thus the effective resistance $R$ of each loop is given by
$\frac{1}{R}=\frac{1}{2}+\frac{1}{4}$
giving $R=(4/3)\Omega$.
Therefore, the equivalent resistance of the network = resistance of four loops connected in series, each having an effective resistance of $(4/3)\Omega =4\times (4/3)=(16/3)\Omega$