Resistance, Resistivity, and Ohm's Law
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AP Physics C: Electricity and Magnetism › Resistance, Resistivity, and Ohm's Law
Considering the information provided, a lightbulb in a household circuit obeys $V=IR$; resistance $R$ (Ω) controls current, and resistivity $\rho$ (in $\Omega\cdot\text{m}$) is intrinsic to the filament material. What happens to current if resistance increases and voltage remains constant according to Ohm’s Law ($V=IR$)?
Resistance decreases as resistivity increases
Current increases as resistance increases
Current decreases as resistance increases
Voltage becomes measured in amperes (A)
Explanation
This question tests understanding of resistance, resistivity, and Ohm's Law in AP Physics C: Electricity and Magnetism. Ohm's Law V = IR shows that for constant voltage, current and resistance have an inverse relationship, expressed as I = V/R. In the lightbulb circuit example, when the filament's resistance increases while the applied voltage remains constant, the current through the bulb must decrease to satisfy Ohm's Law. Choice B is correct because it accurately states that current decreases as resistance increases when voltage is constant, following directly from the mathematical relationship I = V/R. Choice A is incorrect as it suggests a direct relationship between current and resistance, which would violate Ohm's Law and conservation principles. Students should understand that increased resistance means more opposition to current flow, like a dimmer switch increasing resistance to reduce bulb brightness. Practice with real circuits helps: a 60W bulb has lower resistance than a 40W bulb, so it draws more current at the same voltage.
Considering the information provided, a lightbulb in a household circuit follows Ohm’s Law $V=IR$, where $R$ (in $\Omega$) limits $I$ (in A). Resistivity $\rho$ (in $\Omega\cdot\text{m}$) is a material property affecting $R$. What happens to current if resistance increases and voltage remains constant according to $V=IR$?
Current becomes equal to $R$ because $V=IR$
Current remains the same because $V$ is fixed
Current increases because $R$ opposes voltage
Current decreases because $I = V/R$
Explanation
This question tests understanding of resistance, resistivity, and Ohm's Law in AP Physics C: Electricity and Magnetism. Ohm's Law V = IR rearranges to I = V/R, establishing that current is inversely proportional to resistance when voltage remains constant in a circuit. In the lightbulb example, if the filament's resistance increases while the household circuit maintains constant voltage, the current through the bulb must decrease according to the relationship I = V/R. Choice B is correct because it states that current decreases and provides the correct mathematical relationship I = V/R that governs this inverse proportionality. Choice D is incorrect because it misinterprets Ohm's Law - current does not become equal to resistance; rather, current equals voltage divided by resistance, and they have different units (amperes vs ohms). Students should practice dimensional analysis with Ohm's Law to verify relationships and avoid unit confusion. Emphasize that in household circuits, voltage is typically fixed by the power company, making resistance the primary variable for controlling current in devices.
Considering the information provided, a household device follows $V=IR$; resistance $R$ (Ω) is the circuit-level opposition to current, while resistivity $\rho$ (in $\Omega\cdot\text{m}$) is intrinsic to the material. What happens to current if resistance increases and voltage remains constant according to Ohm’s Law ($V=IR$)?
Voltage decreases because $V=I/R$
Current stays constant regardless of $R$
Current decreases because $I=V/R$
Current increases because $I=VR$
Explanation
This question tests understanding of resistance, resistivity, and Ohm's Law in AP Physics C: Electricity and Magnetism. Ohm's Law V = IR can be rearranged to I = V/R, clearly showing that current equals voltage divided by resistance. In the household device example, when resistance increases while voltage stays constant, the current must decrease according to this inverse relationship shown in the equation I = V/R. Choice B is correct because it both states the correct outcome (current decreases) and provides the correct mathematical relationship (I = V/R) that explains why this happens. Choice A is incorrect because it presents a mathematically impossible equation I = VR, which would have incorrect units and suggest current increases with resistance. Students should always check their equation rearrangements using dimensional analysis: I[A] = V[V]/R[Ω] gives correct units, while I = VR would give units of V·Ω, not amperes. Understanding the mathematical form reinforces the conceptual inverse relationship.