An unknown resistor connected across a battery shows a voltage of 12 volts and a current of 4 amperes. What is the resistance?

To determine the resistance of an unknown resistor connected across a battery, Ohm's law is applied, which is defined by the formula:

[ R = \frac{V}{I} ]

where ( R ) is the resistance measured in ohms, ( V ) is the voltage across the resistor measured in volts, and ( I ) is the current flowing through the resistor measured in amperes.

In this scenario, the voltage across the resistor is given as 12 volts, and the current flowing through it is 4 amperes. By substituting these values into the equation, we have:

[ R = \frac{12, \text{volts}}{4, \text{amperes}} = 3, \text{ohms} ]

Therefore, the resistance of the unknown resistor is 3 ohms, making it the correct choice. This illustrates that resistance is directly proportional to voltage and inversely proportional to current. In this case, as the voltage increased while the current was constant, the calculated resistance naturally reflects that relationship.