Resistance, Resistivity, and Ohm's Law - AP Physics C Electricity and Magnetism

1. How is resistance affected by increasing the cross-sectional area of a wire?

   Resistance decreases. Larger area provides more paths for current flow.

2. Define the term 'Ohm's Law'.

   The relationship $V = IR$ describes the proportionality of voltage, current, and resistance. The fundamental principle governing linear electrical circuits.

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

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

4. Identify the unit of resistivity.

   Ohm-meter ($\text{Ω}\text{m}$). Combines resistance unit with length to give material property.

5. State the relationship between voltage and current in Ohm's Law.

   Voltage is directly proportional to current. At constant resistance, voltage and current increase together.

6. What is the formula for voltage drop across a resistor?

   $V = IR$. The potential difference across any resistive element.

7. What is the unit of electrical resistance?

   Ohm ($\text{Ω}$). Named after Georg Ohm, the physicist who discovered Ohm's Law.

8. What does the symbol $\rho$ represent in resistance calculations?

   Resistivity. Greek letter rho denotes the material's intrinsic resistance property.

9. What is the resistance if resistivity is $2 \text{Ω}\text{m}$, length is $4 \text{m}$, and area is $1 \text{m}^2$?

   $R = 8 \text{Ω}$. Using $R = \frac{\rho L}{A} = \frac{2 \times 4}{1} = 8 \text{Ω}$.

10. Find the resistance in a circuit with $V = 12 \text{V}$ and $I = 4 \text{A}$.

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

11. Calculate the voltage if $I = 10 \text{A}$ and $R = 3 \text{Ω}$.

    $V = 30 \text{V}$. Using $V = IR = 10 \times 3 = 30 \text{V}$.

12. What is the resistance of a wire if its length and area are doubled?

    Resistance remains constant. Both length and area scale proportionally, canceling each other.

13. For a fixed voltage, what happens to power if resistance increases?

    Power decreases. From $P = \frac{V^2}{R}$, power is inversely related to resistance.

14. What is the effect on current when voltage is increased and resistance is constant?

    Current increases. Current is directly proportional to voltage at constant resistance.

15. How is resistance related to the dimensions of a material?

    Resistance is proportional to length and inversely to area. From the resistance formula $R = \frac{\rho L}{A}$.

16. Identify the unit of voltage.

    Volt ($\text{V}$). Named after Alessandro Volta, measures electrical potential difference.

17. State the formula for Ohm's Law.

    $V = IR$. The fundamental relationship between voltage, current, and resistance.

18. Define electrical resistivity.

    Resistivity is a material property indicating how strongly it opposes current flow. An intrinsic property that varies by material composition and structure.

19. State the formula to find the power using current and resistance.

    $P = I^2R$. Power formula derived from combining $P = VI$ with Ohm's Law.

20. What happens to the current if voltage is constant and resistance is tripled?

    Current is reduced to one-third. Current is inversely proportional to resistance.

21. Which factor does not affect resistance: length, area, resistivity, or color?

    Color. Only physical properties and geometry affect resistance.

22. State the formula for calculating current using Ohm's Law.

    $I = \frac{V}{R}$. Rearranging Ohm's Law to solve for current.

23. Identify the unit of electric current.

    Ampere ($\text{A}$). The SI base unit for electric current flow.

24. What quantity is represented by the symbol $I$?

    Electric current. Standard symbol for current in electrical equations.

25. What is the relationship between current and resistance in Ohm's Law?

    Current is inversely proportional to resistance. From $V = IR$, current decreases as resistance increases.

26. What happens to resistance if the length of the wire is doubled?

    Resistance doubles. Resistance is directly proportional to length.

27. What is the resistance when $V = 15 \text{V}$ and $I = 3 \text{A}$?

    $R = 5 \text{Ω}$. Using $R = \frac{V}{I} = \frac{15}{3} = 5 \text{Ω}$.

28. What is the formula for power using voltage and resistance?

    $P = \frac{V^2}{R}$. Power formula combining $P = VI$ with $I = \frac{V}{R}$.

29. What symbol is used to denote resistance?

    $R$. Standard symbol representing electrical resistance in circuits.

30. Find the voltage if $I = 5 \text{A}$ and $R = 4 \text{Ω}$.

    $V = 20 \text{V}$. Using $V = IR = 5 \times 4 = 20 \text{V}$.

31. What quantity does the symbol $V$ represent?

    Voltage. Standard symbol for electrical potential difference or voltage.

32. Calculate the current when $V = 24 \text{V}$ and $R = 8 \text{Ω}$.

    $I = 3 \text{A}$. Using $I = \frac{V}{R} = \frac{24}{8} = 3 \text{A}$.

33. What is the effect on resistance if the cross-sectional area is halved?

    Resistance doubles. Resistance is inversely proportional to cross-sectional area.

34. What is the effect of temperature on resistivity in metals?

    Resistivity increases. Thermal energy increases atomic vibrations in metallic conductors.

35. What is the resistance of a wire with resistivity $0.1 \text{Ω}\text{m}$, length $1 \text{m}$, area $0.01 \text{m}^2$?

    $R = 10 \text{Ω}$. Using $R = \frac{\rho L}{A} = \frac{0.1 \times 1}{0.01} = 10 \text{Ω}$.

36. How does resistivity change with temperature in semiconductors?

    Resistivity decreases. Higher temperature increases carrier density in semiconductors.

37. What is the resistivity of a perfect conductor?

    Zero. Perfect conductors offer no resistance to current flow.

38. How does increasing temperature generally affect resistance in conductors?

    Resistance increases. Higher temperature increases atomic vibrations, impeding electron flow.

39. What is the formula for resistance in terms of resistivity?

    $R = \frac{\rho L}{A}$. Shows resistance depends on material properties and geometry.

40. Calculate the resistivity given $R = 10 \text{Ω}$, $L = 2 \text{m}$, $A = 0.5 \text{m}^2$.

    $\rho = 2.5 \text{Ω}\text{m}$. Using $\rho = \frac{RA}{L} = \frac{10 \times 0.5}{2} = 2.5 \text{Ω}\text{m}$.

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