Resistance, Resistivity, and Ohm's Law - AP Physics 2

1. What is the formula for power in terms of current and voltage?

   $P = IV$. Power equals current times voltage.

2. How does increasing length of a wire affect resistance?

   Increases resistance. Longer path means more resistance to current flow.

3. Find $R$ if $P = 100\text{W}$ and $I = 10\text{A}$.

   $R = 1\text{Ω}$. Using $P = I^2R$, so $R = \frac{P}{I^2} = \frac{100}{100} = 1\text{Ω}$.

4. What is Ohm's Law formula?

   $V = IR$. Relates voltage, current, and resistance linearly.

5. Calculate the current if $V = 12\text{V}$ and $R = 4\text{Ω}$.

   $I = 3\text{A}$. Using $I = \frac{V}{R} = \frac{12}{4} = 3\text{A}$.

6. Calculate the power if $I = 5\text{A}$ and $V = 12\text{V}$.

   $P = 60\text{W}$. Using $P = IV = 5 \times 12 = 60\text{W}$.

7. Find the resistivity if $R = 8\text{Ω}$, $L = 4\text{m}$, and $A = 2\text{m}^2$.

   $\rho = 4\text{Ωm}$. Using $\rho = R \frac{A}{L} = 8 \times \frac{2}{4} = 4\text{Ωm}$.

8. What does an increase in cross-sectional area do to resistance?

   Decreases resistance. Larger area provides more parallel paths for current.

9. Calculate resistance using resistivity $\rho = 1.68 \times 10^{-8}\text{Ωm}$, length $L = 2\text{m}$, and area $A = 1\text{m}^2$.

   $R = 3.36 \times 10^{-8}\text{Ω}$. Using $R = \rho \frac{L}{A} = 1.68 \times 10^{-8} \times \frac{2}{1}$.

10. Identify the unit for electric current.

    Ampere ($\text{A}$). Named after André-Marie Ampère.

11. Find $V$ if $I = 3\text{A}$ and $R = 2\text{Ω}$.

    $V = 6\text{V}$. Using $V = IR = 3 \times 2 = 6\text{V}$.

12. How does resistivity change with temperature for metals?

    Increases with temperature. Thermal energy increases atomic vibrations in metals.

13. How is resistivity different from resistance?

    Resistivity is material property; resistance depends on dimensions. Resistivity is intrinsic; resistance includes geometry.

14. What does the variable $V$ represent in Ohm's Law?

    Voltage. The electric potential difference across a component.

15. What does a negative temperature coefficient of resistance mean?

    Resistance decreases with temperature. Negative coefficient means resistance drops as temperature rises.

16. What does the variable $R$ represent in Ohm's Law?

    Resistance. The opposition to current flow in a circuit.

17. Find $I$ if $P = 150\text{W}$ and $V = 30\text{V}$.

    $I = 5\text{A}$. Using $I = \frac{P}{V} = \frac{150}{30} = 5\text{A}$.

18. What is the relationship between resistance and resistivity?

    $R = \rho \frac{L}{A}$. Resistance equals resistivity times length over area.

19. How does resistance vary with temperature for a semiconductor?

    Decreases with temperature. Semiconductors have negative temperature coefficient.

20. What is the formula for power in terms of resistance and current?

    $P = I^2R$. Alternative power formula using current and resistance.

21. Which material has typically lower resistivity, copper or rubber?

    Copper. Copper is an excellent conductor with low resistivity.

22. Calculate the resistance if $V = 10\text{V}$ and $I = 2\text{A}$.

    $R = 5\text{Ω}$. Using $R = \frac{V}{I} = \frac{10}{2} = 5\text{Ω}$.

23. What is the unit of conductance?

    Siemens ($\text{S}$). Named after Ernst Werner von Siemens.

24. What unit is used to measure resistance?

    Ohms ($\text{Ω}$). Named after Georg Ohm, measures opposition to current.

25. What does the symbol $\text{Ω}$ represent?

    Ohm, unit of resistance. Greek letter omega represents the ohm unit.

26. State the formula for resistivity.

    $\rho = R \frac{A}{L}$. Rearranged from $R = \rho \frac{L}{A}$.

27. What is the effect of doubling the cross-sectional area on resistance?

    Resistance is halved. Larger area provides more paths for current flow.

28. What is the unit of power in electric circuits?

    Watt ($\text{W}$). Named after James Watt, measures energy per time.

29. What is one factor that affects resistivity?

    Material. Resistivity depends only on material composition.

30. What is the reciprocal of resistance called?

    Conductance. Conductance $G = \frac{1}{R}$, measures ease of current flow.

31. What does $I$ represent in Ohm's Law?

    Current. The flow of electric charge through a conductor.

32. What happens to resistance if temperature increases?

    Resistance increases. Higher temperature increases atomic vibrations, impeding current.

33. How does material affect resistivity?

    Different materials have different resistivities. Resistivity is an intrinsic material property.

34. What is the relationship between voltage and current if resistance is constant?

    Directly proportional. From Ohm's Law, $V = IR$ with constant $R$.

35. What happens to current if voltage is doubled while resistance is constant?

    Current doubles. From Ohm's Law, current is proportional to voltage.

36. State the formula for power in terms of voltage and resistance.

    $P = \frac{V^2}{R}$. Alternative power formula using voltage and resistance.

37. What is the effect of resistance on current?

    Resistance reduces current. Higher resistance opposes and limits current flow.

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