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A letter A is constructed of a uniform wire of resistance 1 ohm per cm .the sides of the letter are 6cm each and the cross piece in middle is 3cm long. Calculate the resistance batween the ends of the legs.

A letter A is constructed of a uniform wire of resistance 1 ohm per cm .the sides of the letter are 6cm each and the cross piece in middle is 3cm long. Calculate the resistance batween the ends of the legs.

Grade:10

3 Answers

Arun
25750 Points
6 years ago
Dear Nisha
 
SInce the angle subtended is 60 degrees at the apex and both the sides are equal in length, the top of the letter A will make an equilateral triangle. hence all the three sides will be 10 3 cm each and correspondingly will have a resistance of 3 ohms each.
The top triangle in A can be considered as 2 resistors of 3 ohms in series and 1 resistor of 3 ohm in parallel. Effective resistance of this traingle becomes 6/3 = 2 ohms. Now the effective circuit is 3 resistors of 3, 2 and 3 in series. Hence effective resistance is 8 = 8 ohms
 
Regards
Arun (askIITians forum expert)
Gitanjali Rout
184 Points
5 years ago
SInce the angle subtended is 60 degrees at the apex and both the sides are equal in length, the top of the letter A will make an equilateral triangle. hence all the three sides will be 10 3 cm each and correspondingly will have a resistance of 3 ohms each.The top triangle in A can be considered as 2 resistors of 3 ohms in series and 1 resistor of 3 ohm in parallel. Effective resistance of this traingle becomes 6/3 = 2 ohms. Now the effective circuit is 3 resistors of 3, 2 and 3 in series. Hence effective resistance is 8 = 8 ohms
ankit singh
askIITians Faculty 614 Points
3 years ago
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

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