Simple Circuits - AP Physics C Electricity and Magnetism

1. Identify the equivalent capacitance in series $C_1$ and $C_2$.

   $\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2}$. In series, reciprocals of capacitances add.

2. What is the formula for the drift velocity of electrons?

   $v_d = \frac{I}{nqA}$. Average velocity of charge carriers in conductor.

3. What is the formula for electrical energy?

   $E = P \times t$. Energy equals power multiplied by time.

4. What is the unit of electrical resistance?

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

5. Calculate equivalent resistance: $R_1 = 4\text{Ω}$, $R_2 = 6\text{Ω}$ in series.

   $R_{\text{total}} = 10\text{Ω}$. In series: $R_{total} = 4 + 6 = 10\text{Ω}$.

6. What is the formula for resistivity?

   $R = \rho \frac{L}{A}$. Resistance depends on material resistivity, length, and area.

7. What is the unit of electrical current?

   Ampere ($\text{A}$). Named after André-Marie Ampère, measures charge flow rate.

8. What is the formula for energy stored in a capacitor?

   $U = \frac{1}{2}CV^2$. Energy depends on capacitance and voltage squared.

9. Calculate the resistance: $V = 12V$, $I = 4\text{A}$.

   $R = 3\text{Ω}$. Using Ohm's law: $R = V/I = 12/4 = 3\text{Ω}$.

10. What is Kirchhoff's Junction Rule?

    Sum of currents entering a junction equals sum leaving. Conservation of current at any junction point.

11. State the formula for electrical power in a circuit.

    $P = IV$. Power equals voltage times current in any circuit.

12. Calculate power: $V = 12V$, $R = 4\text{Ω}$.

    $P = 36W$. Using $P = V^2/R = 12^2/4 = 36\text{W}$.

13. Identify the equivalent capacitance in parallel $C_1$ and $C_2$.

    $C_{\text{total}} = C_1 + C_2$. In parallel, capacitances simply add together.

14. What is Ohm's Law?

    $V = IR$. Fundamental relationship relating voltage, current, and resistance.

15. What is the unit of capacitance?

    Farad ($\text{F}$). Named after Michael Faraday, measures charge storage ability.

16. Calculate the voltage: $W = 30J$, $Q = 5C$.

    $V = 6V$. Using $V = W/Q = 30/5 = 6\text{V}$.

17. What is Kirchhoff's Loop Rule?

    Sum of voltage drops equals sum of voltage rises in a loop. Conservation of energy around any closed loop.

18. What is the total resistance in series $R_1$ and $R_2$?

    $R_{\text{total}} = R_1 + R_2$. In series, resistances simply add together.

19. Calculate the current: $V = 9V$, $R = 3\text{Ω}$.

    $I = 3\text{A}$. Using Ohm's law: $I = V/R = 9/3 = 3\text{A}$.

20. Calculate equivalent capacitance: $C_1 = 2\text{F}$, $C_2 = 3\text{F}$ in series.

    $C_{\text{total}} = 1.2\text{F}$. In series: $\frac{1}{C} = \frac{1}{2} + \frac{1}{3} = \frac{5}{6}$, so $C = 1.2\text{F}$.

21. Identify the unit of electric charge.

    Coulomb ($\text{C}$). Named after Charles-Augustin de Coulomb, fundamental charge unit.

22. Find the resistance: $P = 200W$, $I = 10A$.

    $R = 2\text{Ω}$. Using $R = P/I^2 = 200/10^2 = 2\text{Ω}$.

23. What is the total resistance in parallel $R_1$ and $R_2$?

    $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}$. In parallel, reciprocals of resistances add.

24. Calculate the charge: $C = 5\text{F}$, $V = 3V$.

    $Q = 15C$. Using $Q = CV = 5 \times 3 = 15\text{C}$.

25. What is the formula for the time constant in an RC circuit?

    $\tau = RC$. Time constant characterizes RC circuit charging/discharging.

26. What is the relationship between power, voltage, and resistance?

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

27. What is the unit of electrical voltage?

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

28. Calculate the time constant: $R = 2\text{Ω}$, $C = 5\text{F}$.

    $\tau = 10s$. Using $\tau = RC = 2 \times 5 = 10\text{s}$.

29. What is the formula for voltage in terms of work and charge?

    $V = \frac{W}{Q}$. Voltage is work per unit charge.

30. Determine power: $V = 10V$, $I = 2\text{A}$.

    $P = 20W$. Using $P = IV = 10 \times 2 = 20\text{W}$.

31. Calculate equivalent capacitance: $C_1 = 2\text{F}$, $C_2 = 3\text{F}$ in parallel.

    $C_{\text{total}} = 5\text{F}$. In parallel: $C_{total} = 2 + 3 = 5\text{F}$.

32. Determine power: $R = 8\text{Ω}$, $I = 2\text{A}$.

    $P = 32W$. Using $P = I^2R = 2^2 \times 8 = 32\text{W}$.

33. Calculate the energy stored: $C = 4\text{F}$, $V = 5V$.

    $U = 50J$. Using $U = \frac{1}{2}CV^2 = \frac{1}{2} \times 4 \times 5^2 = 50\text{J}$.

34. Calculate the voltage: $I = 2\text{A}$, $R = 5\text{Ω}$.

    $V = 10V$. Using Ohm's law: $V = IR = 2 \times 5 = 10\text{V}$.

35. Find the current: $P = 100W$, $V = 10V$.

    $I = 10A$. Using $I = P/V = 100/10 = 10\text{A}$.

36. What is the formula for the charge on a capacitor?

    $Q = CV$. Charge equals capacitance times voltage.

37. Calculate equivalent resistance: $R_1 = 3\text{Ω}$, $R_2 = 6\text{Ω}$ in parallel.

    $R_{\text{total}} = 2\text{Ω}$. In parallel: $\frac{1}{R} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2}$, so $R = 2\text{Ω}$.

38. What is the relationship between power, current, and resistance?

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

39. Calculate the energy used: $P = 60W$, $t = 2h$.

    $E = 432000J$. Convert 2h to 7200s: $E = 60 \times 7200 = 432000\text{J}$.

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