What resistance should be connected in series with a battery of 12.5 volts to trickle-charge it at a 0.5 A rate from a 110-V DC line?

To determine the correct resistance needed to trickle-charge a 12.5-volt battery at a rate of 0.5 A from a 110-V DC line, we start by applying Ohm's Law and the principles of series circuits.

First, we calculate the total voltage drop that must occur across the resistor in order to safely charge the battery. Since the charging voltage is 12.5 V and we are using a 110 V supply, the voltage that needs to be dropped across the resistor can be calculated as follows:

Voltage across the resistor = Supply Voltage - Battery Voltage

= 110 V - 12.5 V

= 97.5 V

Next, applying Ohm's Law, which states that Voltage (V) = Current (I) × Resistance (R), we can rearrange this to find the resistance needed:

Resistance (R) = Voltage (V) / Current (I)

Substituting the values we have:

R = 97.5 V / 0.5 A

= 195 ohms

This calculation shows that a resistance of 195 ohms is required to limit the current to 0.5 A when trickle-charging the 12.5 V battery