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

Options

A. `50.0Omega`
B. `26.7Omega`
C. `2.72Omega`
D. `34.0Omega`

Answer

B

Explanation

A letter .A. with its sides is as shown in the figure. D and E are the mid points of the sides FG and FH respectively. Resistance of side DF is
`=1Omegacm^(-1)xx10cm=10Omega`
Similarly, the resistance of other sides can be calculated and is as shown in the figure. Resistance between D and E is
`=(20xx10)/(20+10)=(20)/(3)Omega`
The resistance between the ends of legs of letter .A. (i.e., between points G and H) is
`=10Omega +(20)/(3)Omega+10Omega=(80)/(3)Omega=26.7Omega`