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:

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:

Quizplus · Accepted Answer

11ecba2d_1319_915e_a3bf_1196cd4400f9_MD0008_00 Conductivity (σ) indicates the ease with which electrons flow within the molecular structure of a material. For example, metals conduct electricity more readily than nonmetals because many of the electrons contained within metals are very loosely associated with the positively charged nuclei. In contrast, the conductivity of electrolytic solutions is proportional to the molar concentration of charged atoms. Conductivity is inversely proportional to resistivity (ρ), a variable that quantifies the relative difficulty with which electrons flow through a material: 11ecba2d_1319_915f_a3bf_75e83a222f44_MD0008_00 Both resistivity and conductivity are intensive properties related to the behavior of materials rather than objects. Therefore, modifying the physical dimensions of an electric conductor may influence the rate at which current flows through the conductor, but not the underlying conductivity of the material from which the conductor is formed. Consequently, conductivity is directly proportional to the conductance of an electric conductor just as resistivity is directly proportional to resistance (R) of a resistor. In this question, a voltage source generates a current (I) through one resistor in a simple circuit. Because resistivity and conductivity are inversely proportional, replacing the resistor with another that has ¼ the conductivity of the original is equivalent to increasing the resistivity of the resistor by a factor of 4. Given that the resistor is otherwise identical (ie, the same physical dimensions), the resistance of the resistor will also increase by a factor of 4. Ohm's law relates the current generated by such a simple circuit to the voltage (V) and resistance: 11ecba2d_1319_b870_a3bf_c7e5e0545c4f_MD0008_00 Therefore, replacing the original resistor with another that has ¼ the conductivity (4 times the resistance and resistivity) of the original will decrease the current traveling through the circuit to ¼ its original value (Choice D). Educational objective: Conductivity is an intensive property that quantifies the ease with which current flows through a material acting as an electric conductor. Conductivity is inversely proportional to resistivity.

Suppose That a Simple Circuit Comprising One Voltage Source and One