To find the resistance when the current is 8 amps, we can use the concept of inverse variation. Inverse variation states that if two values are inversely proportional, their product remains constant. In this case, the resistance and the current are inversely proportional.
Let's set up the equation for inverse variation using the given values:
Resistance × Current = Constant
We can substitute the initial values into this equation:
12 ohms × 4 amps = Constant
Multiplying these two values gives us:
48 = Constant
So, the constant value is 48. Now, we can use this constant to find the resistance when the current is 8 amps:
Resistance × 8 amps = 48
Dividing both sides of the equation by 8:
Resistance = 48 / 8
Simplifying this gives us:
Resistance = 6 ohms
Therefore, the resistance when the current is 8 amps is 6 ohms.