Resistor–Capacitor (RC) Circuits - AP Physics 2
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What is the charge on a capacitor at $t = 0$ when charging begins?
What is the charge on a capacitor at $t = 0$ when charging begins?
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$Q = 0$. Capacitor starts with no charge when charging begins.
$Q = 0$. Capacitor starts with no charge when charging begins.
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State the unit of the time constant $\tau$ in an RC circuit.
State the unit of the time constant $\tau$ in an RC circuit.
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Seconds (s). Time unit from $R$ (ohms) × $C$ (farads) = seconds.
Seconds (s). Time unit from $R$ (ohms) × $C$ (farads) = seconds.
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What is the voltage across a discharging capacitor after one time constant?
What is the voltage across a discharging capacitor after one time constant?
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About 36.8% of initial voltage. After $\tau$, voltage decays to $e^{-1} \approx 0.368$ of initial.
About 36.8% of initial voltage. After $\tau$, voltage decays to $e^{-1} \approx 0.368$ of initial.
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Find the voltage across the capacitor after three time constants during discharge.
Find the voltage across the capacitor after three time constants during discharge.
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Approximately 5% of initial voltage. After $3\tau$, voltage is $e^{-3} \approx 0.05$ of initial.
Approximately 5% of initial voltage. After $3\tau$, voltage is $e^{-3} \approx 0.05$ of initial.
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State the voltage across a capacitor when it is fully charged in an RC circuit.
State the voltage across a capacitor when it is fully charged in an RC circuit.
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Equal to the supply voltage. Fully charged capacitor voltage equals source voltage.
Equal to the supply voltage. Fully charged capacitor voltage equals source voltage.
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How does decreasing the capacitance affect the charging time of an RC circuit?
How does decreasing the capacitance affect the charging time of an RC circuit?
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Decreases charging time. Smaller capacitance reduces time constant, faster charging.
Decreases charging time. Smaller capacitance reduces time constant, faster charging.
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What is the behavior of the current in a discharging RC circuit over time?
What is the behavior of the current in a discharging RC circuit over time?
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Exponential decay. Current follows exponential decay pattern during discharge.
Exponential decay. Current follows exponential decay pattern during discharge.
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Identify the effect of a short circuit across a charged capacitor.
Identify the effect of a short circuit across a charged capacitor.
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Discharges immediately. Short circuit provides zero resistance discharge path.
Discharges immediately. Short circuit provides zero resistance discharge path.
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State the voltage across a capacitor at $t = \infty$ when discharging.
State the voltage across a capacitor at $t = \infty$ when discharging.
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Zero volts (0 V). Capacitor fully discharges to zero voltage eventually.
Zero volts (0 V). Capacitor fully discharges to zero voltage eventually.
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What is the expression for the charge on a capacitor during charging?
What is the expression for the charge on a capacitor during charging?
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$Q(t) = Q_0 (1 - e^{-t/RC})$. Charge builds exponentially toward maximum value $Q_0$.
$Q(t) = Q_0 (1 - e^{-t/RC})$. Charge builds exponentially toward maximum value $Q_0$.
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What is the voltage across the capacitor after five time constants during charging?
What is the voltage across the capacitor after five time constants during charging?
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Approximately equal to $V_0$. After $5\tau$, capacitor reaches 99.3% of final voltage.
Approximately equal to $V_0$. After $5\tau$, capacitor reaches 99.3% of final voltage.
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Calculate the charge on a capacitor at $t = \tau$ during charging.
Calculate the charge on a capacitor at $t = \tau$ during charging.
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$Q = 0.632Q_0$. At one time constant, charge reaches 63.2% of maximum.
$Q = 0.632Q_0$. At one time constant, charge reaches 63.2% of maximum.
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Find the voltage across the capacitor after three time constants during discharge.
Find the voltage across the capacitor after three time constants during discharge.
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Approximately 5% of initial voltage. After $3\tau$, voltage is $e^{-3} \approx 0.05$ of initial.
Approximately 5% of initial voltage. After $3\tau$, voltage is $e^{-3} \approx 0.05$ of initial.
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What is the formula for the time constant in an RC circuit?
What is the formula for the time constant in an RC circuit?
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$\tau = RC$. Product of resistance and capacitance determines RC circuit timing.
$\tau = RC$. Product of resistance and capacitance determines RC circuit timing.
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What is the initial voltage across a capacitor in an uncharged RC circuit?
What is the initial voltage across a capacitor in an uncharged RC circuit?
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Zero volts (0 V). Uncharged capacitor has no stored energy or voltage.
Zero volts (0 V). Uncharged capacitor has no stored energy or voltage.
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What is the voltage across a fully charged capacitor in an RC circuit?
What is the voltage across a fully charged capacitor in an RC circuit?
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Equal to the supply voltage. No current flows when capacitor reaches maximum voltage.
Equal to the supply voltage. No current flows when capacitor reaches maximum voltage.
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What is the effect of adding a resistor in parallel to the existing one in an RC circuit?
What is the effect of adding a resistor in parallel to the existing one in an RC circuit?
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Decreases total resistance. Parallel resistors reduce equivalent resistance, decreasing $\tau$.
Decreases total resistance. Parallel resistors reduce equivalent resistance, decreasing $\tau$.
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Calculate the time constant if $R = 5 \text{ k}\Omega$ and $C = 2 \text{ \muF}$. Provide in milliseconds.
Calculate the time constant if $R = 5 \text{ k}\Omega$ and $C = 2 \text{ \muF}$. Provide in milliseconds.
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$\tau = 10 \text{ ms}$. $\tau = RC = (5000)(2 × 10^{-6}) = 0.01$ s = 10 ms.
$\tau = 10 \text{ ms}$. $\tau = RC = (5000)(2 × 10^{-6}) = 0.01$ s = 10 ms.
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Identify the expression for the voltage across a charging capacitor over time.
Identify the expression for the voltage across a charging capacitor over time.
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$V(t) = V_0 (1 - e^{-t/RC})$. Exponential approach to supply voltage $V_0$.
$V(t) = V_0 (1 - e^{-t/RC})$. Exponential approach to supply voltage $V_0$.
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Determine the time required for a capacitor to discharge to half its initial voltage.
Determine the time required for a capacitor to discharge to half its initial voltage.
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$t = RC \ln(2)$. Half-life formula using natural logarithm of 2.
$t = RC \ln(2)$. Half-life formula using natural logarithm of 2.
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State the voltage across a capacitor at $t = \infty$ when discharging.
State the voltage across a capacitor at $t = \infty$ when discharging.
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Zero volts (0 V). Capacitor fully discharges to zero voltage eventually.
Zero volts (0 V). Capacitor fully discharges to zero voltage eventually.
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What happens to the time constant if the resistance is doubled?
What happens to the time constant if the resistance is doubled?
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Time constant doubles. $\tau = RC$, so doubling $R$ doubles the time constant.
Time constant doubles. $\tau = RC$, so doubling $R$ doubles the time constant.
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How does capacitance affect the time constant in an RC circuit?
How does capacitance affect the time constant in an RC circuit?
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Directly proportional. Larger capacitance increases time constant linearly.
Directly proportional. Larger capacitance increases time constant linearly.
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State the unit of the time constant $\tau$ in an RC circuit.
State the unit of the time constant $\tau$ in an RC circuit.
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Seconds (s). Time unit from $R$ (ohms) × $C$ (farads) = seconds.
Seconds (s). Time unit from $R$ (ohms) × $C$ (farads) = seconds.
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Identify the formula for the voltage across a discharging capacitor.
Identify the formula for the voltage across a discharging capacitor.
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$V(t) = V_0 e^{-t/RC}$. Exponential decay from initial voltage $V_0$.
$V(t) = V_0 e^{-t/RC}$. Exponential decay from initial voltage $V_0$.
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Identify the effect of a short circuit across a charged capacitor.
Identify the effect of a short circuit across a charged capacitor.
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Discharges immediately. Short circuit provides zero resistance discharge path.
Discharges immediately. Short circuit provides zero resistance discharge path.
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Find the time constant if the resistance is $2 \text{ k}\Omega$ and capacitance is $10 \text{ \muF}$.
Find the time constant if the resistance is $2 \text{ k}\Omega$ and capacitance is $10 \text{ \muF}$.
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$\tau = 20 \text{ ms}$. $\tau = RC = (2000)(10 × 10^{-6}) = 0.02$ s = 20 ms.
$\tau = 20 \text{ ms}$. $\tau = RC = (2000)(10 × 10^{-6}) = 0.02$ s = 20 ms.
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What is the expression for the charge on a capacitor during charging?
What is the expression for the charge on a capacitor during charging?
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$Q(t) = Q_0 (1 - e^{-t/RC})$. Charge builds exponentially toward maximum value $Q_0$.
$Q(t) = Q_0 (1 - e^{-t/RC})$. Charge builds exponentially toward maximum value $Q_0$.
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What is the charge on a capacitor at $t = 0$ when charging begins?
What is the charge on a capacitor at $t = 0$ when charging begins?
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$Q = 0$. Capacitor starts with no charge when charging begins.
$Q = 0$. Capacitor starts with no charge when charging begins.
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What is the behavior of the current in a discharging RC circuit over time?
What is the behavior of the current in a discharging RC circuit over time?
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Exponential decay. Current follows exponential decay pattern during discharge.
Exponential decay. Current follows exponential decay pattern during discharge.
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