Amperes (abbreviated amp) measure the strength of electric current. An ohm is the unit of electrical resistance. In an electric circuit, the current varies inversely as the resistance. If the current is 24 amps when the resistance is 20 ohms, find the inverse variation function and use it to find the resistance in ohms when the current is 40 amps.
Please help and work it out thanks
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To find the inverse variation function, we need to determine the relationship between current (I) and resistance (R) using the given information.
According to the problem, the current (I) varies inversely as the resistance (R). Therefore, we can write the inverse variation equation as:
I = k/R
where k is the constant of variation.
To find the value of k, we can substitute the given values of current (I = 24 amps) and resistance (R = 20 ohms) into the equation:
24 = k/20
To solve for k, we can cross-multiply:
24 * 20 = k
k = 480
So, the inverse variation equation for this scenario is:
I = 480/R
Now, to find the resistance (R) when the current is 40 amps, we can plug the new current value (I = 40 amps) into the inverse variation equation:
40 = 480/R
To solve for R, we need to isolate it on one side of the equation. We can begin by cross-multiplying:
40R = 480
Then, we can divide both sides of the equation by 40:
R = 480/40
R = 12
Therefore, when the current is 40 amps, the resistance is 12 ohms.