Sure, let's solve this step-by-step.
1. First, we need to calculate the total resistance in series. In a series circuit, the total resistance is the sum of all the resistances. Here, we have resistors R1, R2, and R3 which are 50, 150, and 150 Ohms respectively. So, the total resistance (R_total) would be R1 + R2 + R3 = 50 Ohms + 150 Ohms + 150 Ohms = 350 Ohms.
2. The next step is to calculate the total current (I_total) flowing through the circuit. We know that the voltage (V) is 12 V. According to Ohm's Law, Current (I_total) = Voltage (V) / Total Resistance (R_total). Hence, the total current is 12V / 350 Ohms ≈ 0.0343 Amps or 34.3 mA.
3. We know that the current flowing through R1 is 0.5 A (500 mA). In series circuits, the current that doesn't go through one component must go through the other components. Thus, the current flowing through R4 would be the total current minus the current through R1. Therefore, the current through R4 (I_R4) is 0.0343 A - 0.5 A = -0.4657 A.
4. The last step is to find the value of R4 using Ohm's Law again. The resistance (R) is equal to the voltage (V) divided by the current (I). However, we know that the current is negative, meaning that it is flowing in the opposite direction. In this case, it is impossible to have a negative resistance (since resistance is always a positive quantity).
The error here seems to be that there is a smaller total current (34.3 mA) as compared to the given current through R1 (500 mA). This discrepancy is hinting that there might be a mistake somewhere in the problem statement, like the values of voltage, resistances or the current through R1, because normally in a series circuit, the current across all components should be the same, as current is a conserved quantity in a circuit.