Twelve wires, each of resistance `1Omega` are connected to form a skeleton cube. Battery of 10V and neglibible internal resistance is connected across diagonally opposite corners of the cube. Determine the equivalent resistance of the network and current supplied by the battery.

Options

A. `5/6 Omega` and 12A
B. `6/5 Omega` and 12 A
C. `5/6 Omega` 4A
D. ` 6/5 Omega` and 4A

Answer

A

Explanation

Let R' be the resistance between point A and H.
`:.V_(AH)=3 I R' ` ...(i)

From figure,
`V_(AH)=V_(AB)+V_(BC)+V_(CH)`
`=IR+(IR)/(2)+I R = (5)/(2) IR ` ... (ii)
From equation (i) and (ii) we have,
`R'=5/6 R = (5)/(6)1 = (5)/(6) Omega`.
From figure,
`3I = (E)/(R')=(10)/((5//6))=(10xx6)/(5)=(60)/(5)`
`3I=12A`