Question

A simple electric circuit has the following properties:

resistance: 12 ohms
voltage: 96 V
Which circuit below has the same current?

(1 point)
Responses

resistance: 8 ohms
voltage: 108 V
resistance: 8 ohms voltage: 108 V

resistance: 6 ohms
voltage: 48 V
resistance: 6 ohms voltage: 48 V

resistance: 4 ohms
voltage: 96 V
resistance: 4 ohms voltage: 96 V

resistance: 12 ohms
voltage: 24 V

Answer 1

To find the current through the original circuit, we can use Ohm's Law, which states that:

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

For the given circuit:

- Resistance \( R = 12 \, \text{ohms} \)
- Voltage \( V = 96 \, \text{V} \)

Calculating the current:

\[ I = \frac{96 \, \text{V}}{12 \, \text{ohms}} = 8 \, \text{A} \]

Now, let's analyze each of the provided options to see which one results in the same current of \( 8 \, \text{A} \):

1. **Resistance: 8 ohms, Voltage: 108 V**
\[
I = \frac{108 \, \text{V}}{8 \, \text{ohms}} = 13.5 \, \text{A}
\]

2. **Resistance: 6 ohms, Voltage: 48 V**
\[
I = \frac{48 \, \text{V}}{6 \, \text{ohms}} = 8 \, \text{A}
\]

3. **Resistance: 4 ohms, Voltage: 96 V**
\[
I = \frac{96 \, \text{V}}{4 \, \text{ohms}} = 24 \, \text{A}
\]

4. **Resistance: 12 ohms, Voltage: 24 V**
\[
I = \frac{24 \, \text{V}}{12 \, \text{ohms}} = 2 \, \text{A}
\]

From the calculations, the option that results in the same current of \( 8 \, \text{A} \) is:

**Resistance: 6 ohms, Voltage: 48 V**