A letter A is made using a uniform wire having resistance 1 Ω per cm. Each side of the letter is 20 cm long, and the middle horizontal piece is 10 cm long. The angle at the top is 60°. Find the equivalent resistance between the two ends of the legs.

First, we understand that resistance depends on the length of the wire. Since the wire has a resistance of 1 ohm per cm:

• 20 cm wire = 20 Ω
• 10 cm wire = 10 Ω

The letter A can be divided into smaller segments. Each side is split into two equal parts, so each small segment becomes 10 cm long, meaning each has 10 Ω resistance.

The middle horizontal wire also has 10 Ω resistance and connects both sides.

Now, observe the connections:

• Some parts are connected in series → resistances are added.
• Some parts are connected in parallel → use formula:
  R = (R? × R?) / (R? + R?)

In the middle section, two paths are in parallel, giving an equivalent resistance of 20/3 Ω.

Adding all resistances:

• Left part = 10 Ω
• Middle part = 20/3 Ω
• Right part = 10 Ω

Total resistance = 10 + 20/3 + 10 = 80/3 Ω