Question

The current in an electrical conductor varies inversely as the resistance of the conductor. What is the current when the resistance is 42 ohms, if the current is 4 amperes when the resistance is 168 ohms?

Answer 1

Current1 / currebt2= Resistance2 / resistance1

x/4A=168 Ohm/ 42 Ohm
x=4*168/42= 16 A

Answer 2

The inverse relationship between the current and the resistance can be expressed as follows, where the product of the current and the resistance is constant:

$(current_1)(resistance_1)=(current_2)(resistance_2)$

Once you establish this relationship, just plug in the numbers given:

$(4 \text{ amperes})(168 \text{ ohms})=(x \text{ amperes})(42 \text{ ohms}) \newline \newline 672=42x \newline \newline x=16 \text{ amperes}$

Another way to think of this is that, in an inverse relationship, if one quantity is multiplied by a certain factor, the other quantity must be divided by that same factor, and vice versa. Since the ohms are being divided by 4:

$\frac{168}{4}=42$

Then the amperes must be multiplied by 4:

$4*4=16$