Explanation: To determine the required series resistance, first calculate the voltage the relay needs to operate. Using Ohm's Law (V = I * R), where I is the current and R is the resistance: 1. **Relay's Operating Voltage (V_relay):** V_relay = 0.125 A (125 mA) * 500 ohms = 62.5 V 2. **Voltage Drop Needed Across Series Resistor (V_series):** The total supply voltage is 110 V. The relay only needs 62.5 V. The remaining voltage must be dropped across the series resistor. V_series = V_supply - V_relay = 110 V - 62.5 V = 47.5 V 3. **Required Series Resistance (R_series):** Since the resistor is in series with the relay, the current through it will also be 125 mA (0.125 A). Using Ohm's Law again (R = V / I): R_series = 47.5 V / 0.125 A = 380 ohms Therefore, a 380-ohm resistor should be connected in series. Options A, B, and D would result in incorrect current levels through the relay, either too high or too low.