Question

A letter A consists of a uniform wire of resistance 1 ohm per cm. The sides of the letter are each 20 cm long and the cross –piec in the middle is 10 cm long while the apex angle is 60 degree. Find the resistance of the letter between the two ends of the legs

Answer 1

Ques

A letter

′

A

′

is constructed of a uniform wire with resistance 1.0Ωcm

−1

. 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

ans:

The circuits are shown above.

Using trignometry,

x

5

=sin30=0.5

⟹ x=10 cm

Thus we get AB=CD=20−10=10 cm

Since all parts are of same length, thus resistance of each part R=10×1=10 Ω

Equivalent circuit is also shown above.

Equivalence resistance between B and E, R

BE

=(10+10)∥10=20∥10

∴ R

eq

=

20+10

20×10

=6.7Ω

Equivalent resistance between A and D, R

AD

=10+6.7+10=26.7Ω

Answer 2

Answer:

80/3

Explanation:

This is based on series and parallel connection of resistances.