To find the current in the initial circuit (with 12 ohms of resistance and 96 V of voltage), we can use Ohm's Law, which states:
\[ I = \frac{V}{R} \]
Where:
- \( I \) is the current (in Amperes),
- \( V \) is the voltage (in Volts),
- \( R \) is the resistance (in Ohms).
For the given circuit:
\[ I = \frac{96 \text{ V}}{12 \text{ ohms}} = 8 \text{ A} \]
Now, we need to find which of the provided circuits yields the same current of 8 A.
-
Resistance: 4 ohms, Voltage: 96 V \[ I = \frac{96 \text{ V}}{4 \text{ ohms}} = 24 \text{ A} \] (not the same)
-
Resistance: 12 ohms, Voltage: 24 V \[ I = \frac{24 \text{ V}}{12 \text{ ohms}} = 2 \text{ A} \] (not the same)
-
Resistance: 6 ohms, Voltage: 48 V \[ I = \frac{48 \text{ V}}{6 \text{ ohms}} = 8 \text{ A} \] (same)
-
Resistance: 8 ohms, Voltage: 108 V \[ I = \frac{108 \text{ V}}{8 \text{ ohms}} = 13.5 \text{ A} \] (not the same)
The circuit that has the same current as the initial circuit is the one with:
Resistance: 6 ohms, Voltage: 48 V.