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  • A letter 'A' is constructed of a uniform wire with resistance  per cm. The sides of the lett

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 peice in the middle is 10 cm long. The apex angle is 60o. The resistance between the ends of the legs is close to :

Option: 1

50.0\; \Omega


Option: 2

10\; \Omega


Option: 3

36.7\; \Omega

 


Option: 4

26.7\; \Omega


Answers (1)

best_answer

Since the angle of the apex is 60, that means the other two angles are also 60 and this is an equilateral triangle.

That means the length from the apex to the cross side is the same as the cross side = 10cm which is 1ohm/cm * 10cm = 10 ohm.

Thus the other wire from the apex to the other side of the cross side is also 10 ohm. Thus the wire in parallel with the cross side is 10+10 = 20 ohms. 
The cross side is 10cm * 1 ohm/cm = 10 ohm 
10 ohms in parallel with 20 ohms: 10||20 = 200/30 = 20/3 ohms. 
The resistance of each leg to the cross side is then 10cm * 1 ohm/cm = 10 ohms.

So the total resistance seen from the legs is 10 + 20/3 + 10 = 80/3 ohms = 26 and 2/3 ohms = 26.67 ohm

Posted by

SANGALDEEP SINGH

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