What resistance is needed for trickle charging a 12.5 V battery at a 0.5 A rate from a 110 V line?

What resistance is needed for trickle charging a 12.5 V battery at a 0.5 A rate from a 110 V line?

• A. 195 ohms
• B. 300 ohms
• C. 95 ohms
• D. None of the above

Answer: (A)

To determine the resistance needed for trickle charging a 12.5 V battery at a rate of 0.5 A from a 110 V line, you can use Ohm's Law and the concept of voltage drop. First, calculate the voltage drop across the resistor necessary to allow the battery to charge properly. The voltage across the resistor can be determined by subtracting the battery voltage from the supply voltage: \[ V_{drop} = V_{supply} - V_{battery} = 110 V - 12.5 V = 97.5 V \] Next, to find the resistance required to achieve the charging current of 0.5 A, you apply Ohm's Law (V = I × R). Rearranging this gives: \[ R = \frac{V_{drop}}{I} = \frac{97.5 V}{0.5 A} = 195 \, \text{ohms} \] This indicates that a resistance of 195 ohms will allow the battery to charge at the desired current level while converting the excess voltage from the supply line to heat in the resistor. The operation at this resistance value ensures that the charging current is controlled, preventing over

To determine the resistance needed for trickle charging a 12.5 V battery at a rate of 0.5 A from a 110 V line, you can use Ohm's Law and the concept of voltage drop.

First, calculate the voltage drop across the resistor necessary to allow the battery to charge properly. The voltage across the resistor can be determined by subtracting the battery voltage from the supply voltage:

[

V_{drop} = V_{supply} - V_{battery} = 110 V - 12.5 V = 97.5 V

]

Next, to find the resistance required to achieve the charging current of 0.5 A, you apply Ohm's Law (V = I × R). Rearranging this gives:

[

R = \frac{V_{drop}}{I} = \frac{97.5 V}{0.5 A} = 195 , \text{ohms}

]

This indicates that a resistance of 195 ohms will allow the battery to charge at the desired current level while converting the excess voltage from the supply line to heat in the resistor. The operation at this resistance value ensures that the charging current is controlled, preventing over