the letter A consists of a uniform wire of resistance 1 ohm/cm. the sides of the letter are 40 cm long and the crosspiece 10 cm. long divides the side in the ratio 1:3 from the apex. find the resistance of the letter between the two ends of the legs.

By question

The crosspiece divided the  side line of A by 1:3 and it meanns that it divide the side into 10:30.

So the resistance on the line segment of 10cm is 10ohms and the resistance on the line segment  of 30cm is 30ohms and it is same for the othe side of A.

Resistance on crosspiece of length 10cm is 10ohms.

So there are three resistance of 10 ohms each and among them two are in series and one is parallel to other two, therefore the equivalent resistance will be 20/3ohms.

Therefore the other two resistance which is of 30ohms are in series with 20/3ohms.

 

Hence the resistance of the letter between the two ends of the legs is