To calculate trickle charging resistance for a 12.5-volt battery from a 110-V DC line, what resistance value is needed at 0.5 A?

To find the correct resistance value for trickle charging a 12.5-volt battery from a 110-volt DC line at a current of 0.5 A, we can use Ohm's law, which is defined by the formula ( V = I \times R ).

In this scenario, we first need to determine the voltage drop across the resistor. Since the battery is at 12.5 volts and the power supply is at 110 volts, the voltage that needs to be dropped across the resistor is calculated as follows:

Voltage across the resistor ( V_R = V_{supply} - V_{battery} = 110V - 12.5V = 97.5V ).

Now that we have the voltage drop, we can employ Ohm's law rearranged to solve for resistance ( R ):

[

R = \frac{V_R}{I} = \frac{97.5V}{0.5A} = 195 \text{ ohms}.

]

This calculation shows that the appropriate resistance needed to achieve a 0.5 A trickle charge while stepping down the voltage from 110 V to 12.5 V is 195 ohms.