Carefully study the circuit diagram shown and calculate the value of `x`.
.

Options

A. 14.3 ohm
B. 11.3 ohm
C. 12 ohm
D. 23.4 ohm

Answer

B

Explanation

The resistances `12 Omega, 6 Omega and 3 Omega` are in parallel. If `R_1` is their resultant resistance, then
`(1)/(R_1)=(1)/(12)+(1)/(6)+(1)/(3) = (2 + 4 + 8)/(24) = (14)/(24) = (7)/(12)` or `R_1 = (12)/(7) Omega`
Since `2 Omega, R_1 and x` are in series,
total resistance in the circuit, `R = 2 + R_1 + x = 2 + (12)/(7) + x = (26)/(7) + x`
From Ohm's law, `I = (V)/( R)` or `0.4 = (6)/(26)/(7)+ x`
or `(26)/(7) + x = (6)/(0.4) = 15` or `x = 15 - (26)/(7) = (79)/(7) Omega = 11.3 Omega`.