The problem describes a situation where the voltage $V$ across a resistor is directly proportional to the current $I$ running through it. The proportionality implies that $V = kI$, where $k$ is the constant of proportionality (resistance).

Step 1: Find the constant of proportionality

Given:

• Current $I_1 = 12$ amps,
• Voltage $V_1 = 480$ volts.

Using the proportionality relationship:

$V_1 = k \times I_1$ $480 = k \times 12$ $k = \frac{480}{12} = 40 \, \Omega$

So the resistance $k = 40 \, \Omega$.

Step 2: Calculate voltage for a different current

Now, we need to find the voltage $V_2$ for a current of $I_2 = 1.5$ amps:

$V_2 = k \times I_2 = 40 \times 1.5 = 60 \, \text{volts}$

Conclusion:

A current of 1.5 amps would produce 60 volts across the same resistor.

Do you need further details on this explanation or have any questions?

Here are 5 related questions you might want to explore:

1. How does resistance affect the relationship between voltage and current?
2. What happens to the voltage if the current is doubled while keeping resistance constant?
3. Can this proportionality be applied to non-linear resistors?
4. How does Ohm's Law apply to this type of circuit?
5. What would the voltage be for a current of 10 amps using the same resistor?

Tip: Remember that in electrical circuits, Ohm's Law ($V = IR$) is key to understanding how voltage, current, and resistance interact.