11.8 Resistor-Capacitor (RC) Circuits

• The capacitor in an RC circuit stores electrical energy
• Increasing the resistance in an RC circuit increases the time constant.
• What is an RC circuit designed to control?

  Charging and discharging
• The time constant represents the time it takes for the capacitor to charge to 63.2% of its maximum voltage.

  True
• The capacitor in an RC circuit discharges to 36.8% of its initial voltage in one time constant.


  True
• What is the formula for the voltage across the capacitor during the charging process in an RC circuit?

  V_{C}(t) = V_{s}(1 - e^{ - t / \tau})</latex>
• What is the time constant of an RC circuit defined as?

  $\tau =$$RC$
• What percentage of the maximum voltage is reached after one time constant \( \tau \)?

  63.2%
• Order the percentages of maximum voltage reached during the charging process based on time in multiples of \( \tau \).

  1️⃣ 0% at \( t = 0 \)

  2️⃣ 63.2% at \( t = \tau \)

  3️⃣ 86.5% at \( t = 2\tau \)

  4️⃣ 95.0% at \( t = 3\tau \)
• The current at time t during the charging process in an RC circuit is given by the formula: I_{0}
• The time constant of an RC circuit is defined by the formula: RC
• The formula for the time constant is τ = RC.


  True
• What is the formula for the voltage across the capacitor during the charging process?

  $V_{C}(t) =$$V_{s}(1 - e^{ - t / \tau})$
• What percentage of the maximum voltage is reached at t = τ during charging?

  63.2%
• The capacitor reaches 63.2% of its maximum voltage in one time constant \(\tau\)
• Order the percentages of maximum voltage reached during charging at different multiples of the time constant:

  1️⃣ 0%

  2️⃣ 63.2%

  3️⃣ 86.5%

  4️⃣ 95.0%
• The current in an RC circuit during charging decays exponentially over time.


  True
• The current in an RC circuit decays exponentially from its initial value to zero
• The voltage across the capacitor during discharging is described by the formula V_{C}(t) = V_{0} e^{ - t / \tau}
• The time constant \(\tau\) is equal to \(RC\)


  True
• $I_{0}$ in the current formula represents the initial current


  True
• In the time constant formula, $R$ is measured in ohms
• Match the application of RC circuits with their description:

  Timing circuits ↔️ Create time delays or oscillations

  Filtering circuits ↔️ Remove high-frequency signals

  Differentiating circuits ↔️ Process input signals

  Voltage regulation ↔️ Provide stable power supply
• What is the time constant (τ) of an RC circuit defined as?

  $\tau =$$RC$
• What type of behavior does an RC circuit exhibit due to the interaction between resistors and capacitors?

  Time-dependent behavior
• During the charging process in an RC circuit, the voltage across the capacitor increases according to an exponential function.
• The source voltage in an RC circuit remains constant during the charging process.


  True
• The voltage across the capacitor at time t during the charging process is given by the formula: V_{s}
• What percentage of the initial current remains after \( 4\tau \)?

  1.8%
• The time constant (τ) of an RC circuit is a measure of the time it takes for the capacitor to charge or discharge
• Increasing the resistance in an RC circuit increases the time constant.


  True
• Match the time with the percentage of maximum voltage reached during charging:

  $t =$$0$ ↔️ 0%

  $t =$$\tau$ ↔️ 63.2%

  $t =$$2\tau$ ↔️ 86.5%
• What does \(V_s\) represent in the charging voltage formula?

  Source voltage
• The current in an RC circuit during charging decreases to 36.8% of its initial value after one time constant \(\tau\)
• What is the formula for the voltage across the capacitor during the discharging process?

  $V_{C}(t) =$$V_{0} e^{ - t / \tau}$
• During the discharging process in an RC circuit, the voltage across the capacitor increases over time

  False
• Match the time with the percentage of initial voltage during discharging:

  $t =$$0$ ↔️ 100%

  $t =$$\tau$ ↔️ 36.8%

  $t =$$2\tau$ ↔️ 13.5%

  $t =$$3\tau$ ↔️ 5.0%
• What is the formula for the current during discharging in an RC circuit?

  I(t) = I_{0} e^{ - t / \tau}</latex>
• What is the formula for the time constant in an RC circuit?

  $\tau =$$RC$
• The time constant determines how quickly a capacitor charges to 63.2% of its full voltage


  True