From the diagram above, determine the value of the resistance X

Explanation

Let the combined parallel resistance of 3 Ω and x = Q Ω
∴ Total resistance in the circuit = 2 + Q + 1.5 = 3.5 + Q Ω
Total current in the circuit = 2A
P.D a cross the circuit 12 volts
∴ From Ohm’s law, V = IR
12 = 2(3.5 + Q)
= 7.0 + 2Q
∴ 2Q = 12 – 7
= 5
∴ Q = ⁵/₂ = 2.5 Ω
Thus from parallel formula: I/Q = 1/3 + 1/x
¹/_2.5 = ¹/₃ + ¹/_x
∴ ¹/_x = ¹/_2.5 - ¹/₃ = ^3-2.5/_7.5 = ^0.5/_7.5
X = ^7.5/_0.5 = ⁷⁵/₅ = 15 Ω
∴ X = 15 Ω