AP Physics 2 Flashcards: Resistor Capacitor Rc Circuits

What this deck covers

This deck focuses on Resistor Capacitor Rc Circuits, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: State the expression for the current in an RC circuit during charging.

Answer: $I(t) = \frac{V_0}{R} e^{-t/RC}$. Current decays exponentially from initial value $\frac{V_0}{R}$.

Flashcard 2: State the voltage across a capacitor when it is fully charged in an RC circuit.

Answer: Equal to the supply voltage. Fully charged capacitor voltage equals source voltage.

Flashcard 3: What is the effect of adding a resistor in parallel to the existing one in an RC circuit?

Answer: Decreases total resistance. Parallel resistors reduce equivalent resistance, decreasing $\tau$.

Flashcard 4: Find the voltage across the capacitor after three time constants during discharge.

Answer: Approximately 5% of initial voltage. After $3\tau$, voltage is $e^{-3} \approx 0.05$ of initial.

Flashcard 5: What is the charge on a capacitor at $t = 0$ when charging begins?

Answer: $Q = 0$. Capacitor starts with no charge when charging begins.

Flashcard 6: Identify the initial current through a capacitor when discharging begins.

Answer: $\frac{V_0}{R}$. Same as charging current but in opposite direction.

Flashcard 7: Identify the expression for the voltage across a charging capacitor over time.

Answer: $V(t) = V_0 (1 - e^{-t/RC})$. Exponential approach to supply voltage $V_0$.

Flashcard 8: What is the charge on a capacitor at $t = 0$ when charging begins?

Answer: $Q = 0$. Capacitor starts with no charge when charging begins.

Flashcard 9: State the unit of the time constant $\tau$ in an RC circuit.

Answer: Seconds (s). Time unit from $R$ (ohms) × $C$ (farads) = seconds.

Flashcard 10: What is the initial voltage across a capacitor after a switch is closed in an RC circuit?

Answer: Zero volts (0 V). Capacitor starts uncharged when switch closes.

Flashcard 11: What happens to the time constant if capacitance is reduced by half?

Answer: Time constant is halved. $\tau = RC$, so halving $C$ halves the time constant.

Flashcard 12: Identify the expression for the voltage across a charging capacitor over time.

Answer: $V(t) = V_0 (1 - e^{-t/RC})$. Exponential approach to supply voltage $V_0$.

Flashcard 13: What is the energy stored in a fully charged capacitor?

Answer: $E = \frac{1}{2}CV^2$. Energy formula for charged capacitor's electric field.

Flashcard 14: State the relationship between voltage and charge for a capacitor.

Answer: $V = \frac{Q}{C}$. Fundamental capacitor equation relating charge and voltage.

Flashcard 15: Which component stores energy in an RC circuit?

Answer: Capacitor. Capacitor stores electrical energy in electric field.

Flashcard 16: Determine the time required for a capacitor to discharge to half its initial voltage.

Answer: $t = RC \ln(2)$. Half-life formula using natural logarithm of 2.

Flashcard 17: How does capacitance affect the time constant in an RC circuit?

Answer: Directly proportional. Larger capacitance increases time constant linearly.

Flashcard 18: Calculate the time constant if $R = 5 \text{ k}\Omega$ and $C = 2 \text{ \muF}$. Provide in milliseconds.

Answer: $\tau = 10 \text{ ms}$. $\tau = RC = (5000)(2 × 10^{-6}) = 0.01$ s = 10 ms.

Flashcard 19: What is the initial voltage across a capacitor after a switch is closed in an RC circuit?

Answer: Zero volts (0 V). Capacitor starts uncharged when switch closes.

Flashcard 20: State the expression for the current in an RC circuit during charging.

Answer: $I(t) = \frac{V_0}{R} e^{-t/RC}$. Current decays exponentially from initial value $\frac{V_0}{R}$.

Flashcard 21: Calculate the charge on a capacitor at $t = \tau$ during charging.

Answer: $Q = 0.632Q_0$. At one time constant, charge reaches 63.2% of maximum.

Flashcard 22: Identify the effect of a short circuit across a charged capacitor.

Answer: Discharges immediately. Short circuit provides zero resistance discharge path.

Flashcard 23: What is the voltage across the capacitor after five time constants during charging?

Answer: Approximately equal to $V_0$. After $5\tau$, capacitor reaches 99.3% of final voltage.

Flashcard 24: Calculate the time constant if $R = 5 \text{ k}\Omega$ and $C = 2 \text{ \muF}$. Provide in milliseconds.

Answer: $\tau = 10 \text{ ms}$. $\tau = RC = (5000)(2 × 10^{-6}) = 0.01$ s = 10 ms.

Flashcard 25: What is the time to reach 99% of the final charge in an RC circuit?

Answer: Approximately $5\tau$. Practical time for essentially complete charging/discharging.

Flashcard 26: What is the current in an RC circuit immediately after a switch is closed?

Answer: $\frac{V_0}{R}$. Maximum current flows when capacitor acts like short circuit.

Flashcard 27: Determine the energy dissipated by the resistor during capacitor discharge.

Answer: Equal to initial capacitor energy. All stored energy converts to heat in resistor.

Flashcard 28: What is the expression for the charge on a capacitor during charging?

Answer: $Q(t) = Q_0 (1 - e^{-t/RC})$. Charge builds exponentially toward maximum value $Q_0$.

Flashcard 29: Find the time constant if the resistance is $2 \text{ k}\Omega$ and capacitance is $10 \text{ \muF}$.

Answer: $\tau = 20 \text{ ms}$. $\tau = RC = (2000)(10 × 10^{-6}) = 0.02$ s = 20 ms.

Flashcard 30: What happens to the time constant if the resistance is doubled?

Answer: Time constant doubles. $\tau = RC$, so doubling $R$ doubles the time constant.

Flashcard 31: Find the time constant if the resistance is $2 \text{ k}\Omega$ and capacitance is $10 \text{ \muF}$.

Answer: $\tau = 20 \text{ ms}$. $\tau = RC = (2000)(10 × 10^{-6}) = 0.02$ s = 20 ms.

Flashcard 32: Identify the formula for the voltage across a discharging capacitor.

Answer: $V(t) = V_0 e^{-t/RC}$. Exponential decay from initial voltage $V_0$.

Flashcard 33: What is the voltage across a discharging capacitor after one time constant?

Answer: About 36.8% of initial voltage. After $\tau$, voltage decays to $e^{-1} \approx 0.368$ of initial.

Flashcard 34: Identify the initial current through a capacitor when discharging begins.

Answer: $\frac{V_0}{R}$. Same as charging current but in opposite direction.

Flashcard 35: What percentage of the final voltage is reached at one time constant?

Answer: About 63.2%. At $t = \tau$, $e^{-1} \approx 0.368$, so $1 - e^{-1} \approx 0.632$.

Flashcard 36: In an RC circuit, what does a larger resistor value do to the charging time?

Answer: Increases charging time. Higher resistance increases time constant, slower charging.

Flashcard 37: State the voltage across a capacitor at $t = \infty$ when discharging.

Answer: Zero volts (0 V). Capacitor fully discharges to zero voltage eventually.

Flashcard 38: What is the voltage across a fully charged capacitor in an RC circuit?

Answer: Equal to the supply voltage. No current flows when capacitor reaches maximum voltage.

Flashcard 39: How does capacitance affect the time constant in an RC circuit?

Answer: Directly proportional. Larger capacitance increases time constant linearly.

Flashcard 40: What is the initial voltage across a capacitor in an uncharged RC circuit?

Answer: Zero volts (0 V). Uncharged capacitor has no stored energy or voltage.

Flashcard 41: How does decreasing the capacitance affect the charging time of an RC circuit?

Answer: Decreases charging time. Smaller capacitance reduces time constant, faster charging.

Flashcard 42: How does decreasing the capacitance affect the charging time of an RC circuit?

Answer: Decreases charging time. Smaller capacitance reduces time constant, faster charging.

Flashcard 43: What is the initial voltage across a capacitor in an uncharged RC circuit?

Answer: Zero volts (0 V). Uncharged capacitor has no stored energy or voltage.

Flashcard 44: What is the current through the resistor at $t = \infty$ in a charging RC circuit?

Answer: Zero amperes (0 A). No current flows when capacitor is fully charged.

Flashcard 45: What happens to the time constant if the resistance is doubled?

Answer: Time constant doubles. $\tau = RC$, so doubling $R$ doubles the time constant.

Flashcard 46: What is the current in an RC circuit immediately after a switch is closed?

Answer: $\frac{V_0}{R}$. Maximum current flows when capacitor acts like short circuit.

Flashcard 47: State the voltage across a capacitor at $t = \infty$ when discharging.

Answer: Zero volts (0 V). Capacitor fully discharges to zero voltage eventually.

Flashcard 48: Identify the effect of a short circuit across a charged capacitor.

Answer: Discharges immediately. Short circuit provides zero resistance discharge path.

Flashcard 49: What percentage of the final voltage is reached at one time constant?

Answer: About 63.2%. At $t = \tau$, $e^{-1} \approx 0.368$, so $1 - e^{-1} \approx 0.632$.

Flashcard 50: Determine the energy dissipated by the resistor during capacitor discharge.

Answer: Equal to initial capacitor energy. All stored energy converts to heat in resistor.

Flashcard 51: What is the behavior of the current in a discharging RC circuit over time?

Answer: Exponential decay. Current follows exponential decay pattern during discharge.

Flashcard 52: What is the behavior of the current in a discharging RC circuit over time?

Answer: Exponential decay. Current follows exponential decay pattern during discharge.

Flashcard 53: What is the time to reach 99% of the final charge in an RC circuit?

Answer: Approximately $5\tau$. Practical time for essentially complete charging/discharging.

Flashcard 54: State the relationship between voltage and charge for a capacitor.

Answer: $V = \frac{Q}{C}$. Fundamental capacitor equation relating charge and voltage.

Flashcard 55: Which law applies to the sum of voltages in an RC circuit loop?

Answer: Kirchhoff's Voltage Law. Voltage drops must sum to zero around any closed loop.

Flashcard 56: What is the voltage across a discharging capacitor after one time constant?

Answer: About 36.8% of initial voltage. After $\tau$, voltage decays to $e^{-1} \approx 0.368$ of initial.

Flashcard 57: Which component stores energy in an RC circuit?

Answer: Capacitor. Capacitor stores electrical energy in electric field.

Flashcard 58: What is the formula for the time constant in an RC circuit?

Answer: $\tau = RC$. Product of resistance and capacitance determines RC circuit timing.

Flashcard 59: State the unit of the time constant $\tau$ in an RC circuit.

Answer: Seconds (s). Time unit from $R$ (ohms) × $C$ (farads) = seconds.

Flashcard 60: State the voltage across a capacitor when it is fully charged in an RC circuit.

Answer: Equal to the supply voltage. Fully charged capacitor voltage equals source voltage.

Flashcard 61: Find the voltage across the capacitor after three time constants during discharge.

Answer: Approximately 5% of initial voltage. After $3\tau$, voltage is $e^{-3} \approx 0.05$ of initial.

Flashcard 62: Identify the formula for the voltage across a discharging capacitor.

Answer: $V(t) = V_0 e^{-t/RC}$. Exponential decay from initial voltage $V_0$.

Flashcard 63: In an RC circuit, what does a larger resistor value do to the charging time?

Answer: Increases charging time. Higher resistance increases time constant, slower charging.

Flashcard 64: Calculate the charge on a capacitor at $t = \tau$ during charging.

Answer: $Q = 0.632Q_0$. At one time constant, charge reaches 63.2% of maximum.

Flashcard 65: What is the voltage across a fully charged capacitor in an RC circuit?

Answer: Equal to the supply voltage. No current flows when capacitor reaches maximum voltage.

Flashcard 66: Determine the time required for a capacitor to discharge to half its initial voltage.

Answer: $t = RC \ln(2)$. Half-life formula using natural logarithm of 2.

Flashcard 67: What is the expression for the charge on a capacitor during charging?

Answer: $Q(t) = Q_0 (1 - e^{-t/RC})$. Charge builds exponentially toward maximum value $Q_0$.

Flashcard 68: What is the voltage across the capacitor after five time constants during charging?

Answer: Approximately equal to $V_0$. After $5\tau$, capacitor reaches 99.3% of final voltage.

Flashcard 69: What is the energy stored in a fully charged capacitor?

Answer: $E = \frac{1}{2}CV^2$. Energy formula for charged capacitor's electric field.

Flashcard 70: What is the effect of adding a resistor in parallel to the existing one in an RC circuit?

Answer: Decreases total resistance. Parallel resistors reduce equivalent resistance, decreasing $\tau$.

Flashcard 71: What is the formula for the time constant in an RC circuit?

Answer: $\tau = RC$. Product of resistance and capacitance determines RC circuit timing.

Flashcard 72: Which law applies to the sum of voltages in an RC circuit loop?

Answer: Kirchhoff's Voltage Law. Voltage drops must sum to zero around any closed loop.