Question

A wire of resistance 20ohm is bent to form a regular pentagon ABCDE. What will be the resistance between the points A and B?

• A. 16 ohm
• B. 4 ohm
• C. 1.6 ohm
• D. 3.2 ohm

Answer 1

The correct option is D

3.2 ohm

Let us consider AE, ED, DC, CB, and AB as individual resistors of resistance 4ohm each. We can see that AE, ED, DC, CBare connected in series which and the total of them is in parallel with AB. So net resistance = $\frac{1}{R_{net}}=\frac{1}{16}+\frac{1}{4}$
$\frac{1}{16}+\frac{1}{4}$
$R_{net}=3.2ohm$