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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

A

`50.0 Omega`

B

`10 Omega`

C

`36.7 Omega`

D

`26.7 Omega`

Text Solution

Verified by Experts

The correct Answer is:
D

For ADE `(1)/(R.) = (1)/(2x) + (1)/(10)` or `(R.) = (20 x)/(10+2x)`
`R_(BC) = (20 x)/(10 + 2x)+ 20-x+ 20 - x... (i)`
or `(20 x)/(10+2x) + 40 = 2x`
Solving we get `x= 10 Omega`
Putting the value of `x^(-) 10 Omega` in equation (i)
We get
`R_(BC)= (20 xx 10)/(10 +2 xx 10)+ 20 - 10 = (80)/(3) = 26.7 Omega`
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