Question

A letter 'A' is constructed of a uniform wire with resistance 1.0 \( \Omega \) per cm. The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60°. The resistance between the ends of the legs is close to:

• A. 50.0 \( \Omega \)
• B. 10 \( \Omega \)
• C. 36.7 \( \Omega \)
• D. 26.7 \( \Omega \)

Hint:

The total resistance in a complex shape like a letter 'A' can be found by summing the resistances in each leg and applying series and parallel combinations.

Answer 1

The Correct Option is D

Step 1: Calculate resistance in the legs.
The total resistance between the ends of the legs is the sum of the resistance in the individual legs. Since the resistance per cm is given, we can use the geometry of the letter 'A' to calculate the total resistance. After solving, we get a resistance of 26.7 \( \Omega \).
Thus, the correct answer is (4).