In a series circuit, current does not divide; it remains constant throughout all components. This current is determined by Ohm's Law, expressed as \(V= IR\), or rearranged to \(I=\frac VR\). Here, R represents the total equivalent resistance. The resistances provided are 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω, and 12 Ω, all connected in series. Consequently, the total resistance R is the sum of these individual resistances: R = 0.2 + 0.3 + 0.4 + 0.5 + 12 = 13.4 Ω. Given a potential difference V = 9 V, the current I is calculated as I = \(\frac {9}{13.4}\) = 0.671 A.
Thus, the current flowing through the 12 Ω resistor is 0.671 A.