11.6 RC Circuits

• A capacitor in an RC circuit stores electrical energy.


  True
• What percentage of its full capacity does a capacitor charge to in one time constant (τ)?

  63.2%
• Arrange the resistor and capacitor values in order of increasing time constant (τ):

  1️⃣ 100 Ω and 100 μF

  2️⃣ 1 kΩ and 10 μF

  3️⃣ 10 kΩ and 1 μF
• During charging, the voltage across the capacitor increases over time, while the current decreases.


  True
• The current in an RC circuit increases exponentially during charging.

  False
• The equation for the current in an RC circuit during charging is I(t) = \frac{V_{\in}}{R} e^{ - t / \tau}</latex>, where $V_{\in}$ is the input voltage
• The equation for the voltage across a capacitor during discharging is $V_{C}(t) =$$V_{0} e^{ - t / \tau}$, where V_{0}</latex> is the initial voltage
• The time constant $\tau$ in an RC circuit is equal to the product of resistance and capacitance
• The time constant in an RC circuit is calculated using the formula τ = RC
• What determines how quickly a capacitor discharges in an RC circuit?

  Time constant τ
• The voltage across a capacitor during charging is given by the equation V_{C}(t) = V_{\in}(1 - e^{ - t / \tau})
• A larger time constant in an RC circuit results in a slower charging rate.


  True
• What happens to the voltage and current in an RC circuit during charging?

  Voltage increases, current decreases
• The time constant in an RC circuit determines how quickly the voltage and current change during charging.


  True
• What is the equation for the current in an RC circuit during charging?

  I(t) = \frac{V_{\in}}{R} e^{ - t / \tau}</latex>
• During discharging of an RC circuit, the voltage across the capacitor decreases exponentially.
• A resistor in an RC circuit controls the flow of current
• A larger time constant in an RC circuit results in faster charging and discharging.

  False
• What is the definition of a time constant (τ) in an RC circuit?

  Time to reach 63.2% charge
• What is the equation for voltage across a capacitor during charging in an RC circuit?

  V_{C}(t) = V_{\in}(1 - e^{ - t / \tau})</latex>
• What happens to the voltage across a capacitor during the charging of an RC circuit?

  It increases exponentially
• What is the formula for the time constant in an RC circuit?

  $\tau =$$RC$
• What happens to the voltage across a capacitor during the discharging of an RC circuit?

  It decreases exponentially
• What does $V_{0}$ represent in the discharging voltage equation of an RC circuit?


  Initial voltage
• What are the two primary components of an RC circuit?

  Resistor and capacitor
• The voltage across a capacitor during discharging is given by the equation V_{C}(t) = V_{0}e^{ - t / \tau}
• What happens to the voltage across a capacitor during the charging of an RC circuit?

  Increases exponentially
• A higher time constant in an RC circuit results in a faster charging rate.

  False
• What is the current equation in an RC circuit during charging?

  I(t) = (V_in/R)e^-t/τ
• In the charging equation, $\tau$ represents the time constant.
• Arrange the charging times in increasing order of voltage across the capacitor:

  1️⃣ 0τ

  2️⃣ 1τ

  3️⃣ 2τ

  4️⃣ 3τ
• The time constant (τ) in discharging determines the rate of voltage decrease.


  True
• A larger time constant τ in an RC circuit results in a slower discharge.

  True
• What is the equation describing the voltage behavior during the discharging of an RC circuit?

  $V_{C}(t) =$$V_{0} e^{ - t / \tau}$
• Both voltage and current decrease exponentially during the discharge of an RC circuit.


  True
• A larger time constant in an RC circuit results in a slower discharge.


  True
• The time constant τ determines how quickly the capacitor charges or discharges.
• What does the universal time constant (τ) represent in an RC circuit?

  Time to 63.2% capacity
• Order the time intervals based on the percentage of voltage across the capacitor in an RC circuit:

  1️⃣ 0τ: 0% of V_in

  2️⃣ 1τ: 63.2% of V_in

  3️⃣ 2τ: 86.5% of V_in

  4️⃣ 3τ: 95.0% of V_in

  5️⃣ 4τ: 98.2% of V_in
• The current in an RC circuit decreases to 13.5% of its maximum value at time 2τ.

  True