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A letter A is constructed as a uniform w...

A letter `A` is constructed as a uniform wire of resistance 1 ohm/cm. The sides of the letter are 20 cm long and the cross piece in the middle is 10 cm long while the vertex angle is `60^(@)` the resistance of the letter between the two ends of the legs is

Text Solution

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Here, resistance of length `1 cm = 1 Omega`
Resistance of length `20 cm=20 Omega`
It means, the resistance of legs AC and AE are `20 Omega` each
Resistance of cross piece of length 10 cm
`=10 Omega`
As cross-piece is in the middle of each leg, so
`AB = BC = AD = DE = BD=10 cm`
The resistance of each is `10 Omega` as shown in figure
The series resistance of arms BA and `AD(=10 +10 =20 Omega)` is in parallel to the resistance of arm `BD(= 10 Omega)` so effective resistance between
B and D, `R'=(10 xx 20)/(10 + 20) =200/30 =20/3 Omega`
Now the resistance of arm CB, R' and of arm DE are in series. Therefore, equivalent resistance between `CE = 10 + 20/3 +10 = 80/3 = 26.67 Omega`
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