Explanation: To trickle-charge a battery, a series resistor is used to drop the excess voltage from the source and limit the charging current. First, determine the voltage drop required across the series resistor. This is the difference between the source voltage and the battery's terminal voltage: Voltage Drop (V_R) = Source Voltage - Battery Voltage V_R = 110 V - 12.5 V = 97.5 V Next, apply Ohm's Law (R = V/I) to find the resistance needed to drop 97.5 V while allowing a 0.5 A current: Resistance (R) = V_R / Charging Current R = 97.5 V / 0.5 A = 195 ohms Connecting a 195-ohm resistor in series ensures the battery is charged at the desired 0.5 A rate, preventing overcurrent and potential damage to the battery. Options A and B would result in significantly higher or lower charging currents, respectively.