Final answer:
To find the current through a 12 Ω resistor in a circuit, we use Ohm's Law to first determine the total current in the circuit and the voltage drop across the first resistor. Then we calculate the parallel voltage and apply Ohm's Law again to find the current through the resistor in question.
Step-by-step explanation:
The question being asked pertains to Physics, and more specifically to a concept within electrical circuits involving Ohm's Law. To find the current through the 12 Ω resistor, we use the information given about the voltage across the resistor and the total current in the circuit. According to the details provided, we first need to determine the total current (I) in the circuit using Ohm's Law, which relates the total voltage (V) and the total resistance (Rtot). In this case, with a total voltage of 12.0 V and a total resistance of 5.11 Ω, the total current is calculated as I = V / Rtot = 12.0 V / 5.11 Ω = 2.35 A.
Next, we calculate the voltage drop across the first resistor (V1). Once we know V1, we can find the reduced voltage applied to the parallel combination of resistors (R2 and R3), defined as Vp. Vp can be calculated as the initial voltage minus the voltage drop V1, giving us Vp = V - V1. For example, if V1 is 2.35 V, and the initial voltage is 12.0 V, then Vp = 12.0 V - 2.35 V = 9.65 V.
Finally, with the voltage across R2 (Vp), we can determine the current through R2 (I2) using Ohm's Law: I2 = Vp / R2. For a resistor value of R2 = 6.00 Ω, and Vp = 9.65 V, the current through R2 would be I2 = 9.65 V / 6.00 Ω = 1.61 A.