The resistance in an electric circuit varies inversely with the current. If the resistance is 12 ohms when the current is 4 amps, what is the resistance when the current is 8 amps.?

R = kI, where k is a constant.

put in the given values
12 = k(4)
k = 3

Now you have your equation to answer the last part

21

A

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.