We are asked to determine the values of the currents.
Since the 4 Ohms resistance is parallel to the 12v voltage source this means that the voltage through this resistance is also 12 V. We can determine the current using Ohm's law:
[tex]I_2=\frac{V}{R_2}[/tex]Now, we plug in the values:
[tex]I_2=\frac{12V}{4\Omega}[/tex]Solving the operations:
[tex]I_2=3A[/tex]Now, since the 6 Ohms and 8 Ohms resistors are also parallel to the voltage source, the voltage through these resistors is 12V. We can determine the current also using Ohm's law:
[tex]I_3=\frac{V}{R_3}[/tex]The resistance is the equivalent resistance. Since the resistors are connected in parallel this means that the total resistance is the sum of both resistances:
[tex]R_3=6\Omega+8\Omega=14\Omega[/tex]Now, we substitute and we get:
[tex]I_3=\frac{12V}{14\Omega}=0.86A[/tex]Now, currents 3 and 2 add up to current 1, therefore:
[tex]I_1=I_2+I_3[/tex]Substituting the values:
[tex]I_1=3A+0.86A=3.86A[/tex]Therefore, the current 1 is 3.86 Amperes.