Suppose that a simple circuit comprising one voltage source and one metallic resistor yields current I. If the resistor were replaced with another resistor that is identical except that it has 75% lower conductivity, then I would:A.increase by a factor of 2.B.increase by a factor of 4.C.decrease by a factor of 2.D.decrease by a factor of 4.
Question
Suppose that a simple circuit comprising one voltage source and one metallic resistor yields current I. If the resistor were replaced with another resistor that is identical except that it has 75% lower conductivity, then I would:A.increase by a factor of 2.B.increase by a factor of 4.C.decrease by a factor of 2.D.decrease by a factor of 4.
Solution
The relationship between current (I), voltage (V), and resistance (R) in a circuit is given by Ohm's Law, which states that I = V/R.
If the conductivity of the resistor decreases by 75%, this means that the resistance of the resistor increases by a factor of 4 (since conductivity and resistance are inversely proportional).
Substituting this into Ohm's Law, we get I = V/(4R).
This means that the current would decrease by a factor of 4.
So, the correct answer is D. decrease by a factor of 4.
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