Question

What is the equivalent resistance of the network shown in figure? The numbers indicate resistance in ohms

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

Answer 1

The correct option is B $\frac{16}{3}$ ohm

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