11.6 RC Circuits

• What components does an RC circuit typically consist of?

  Resistor and capacitor
• What does the time constant (τ) in an RC circuit indicate?

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

  63.2%
• What is the definition of a time constant (τ) in an RC circuit?

  Time to reach 63.2% charge
• What effect does a higher time constant have on the charging of a capacitor?

  Slower charging
• What percentage of the input voltage does the capacitor reach after one time constant during charging?

  63.2%
• 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
• A resistor in an RC circuit controls the flow of current
• The time constant in an RC circuit is calculated using the formula τ = RC
• The time constant (τ) in an RC circuit increases if either the resistance (R) or capacitance (C) increases.


  True
• 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
• 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 is the current in an RC circuit after one time constant during charging, expressed as a percentage of its initial value?

  36.8%
• The equation for the voltage across a capacitor during charging is V_{C}(t) = V_{\in}(1 - e^{ - t / \tau})</latex>, where $\tau$ is the time constant
• Arrange the following time intervals in order of increasing voltage across the capacitor during charging:

  1️⃣ 0τ

  2️⃣ 1τ

  3️⃣ 2τ

  4️⃣ 3τ

  5️⃣ 4τ
• 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
• What does $V_{0}$ represent in the discharging voltage equation of an RC circuit?


  Initial voltage
• What effect does a larger time constant have on the discharge rate of a capacitor?

  It slows it down
• The time constant in an RC circuit increases if the resistance increases.


  True
• What determines how quickly a capacitor discharges in an RC circuit?

  Time constant τ
• What happens to the voltage across a capacitor during the charging of an RC circuit?

  Increases exponentially
• Arrange the time intervals in increasing order of the percentage of input voltage reached across the capacitor during charging.

  1️⃣ 1τ

  2️⃣ 2τ

  3️⃣ 3τ

  4️⃣ 4τ
• The time constant is calculated using the formula τ = RC
• The voltage equation during charging is V_{C}(t) = V_{\in}(1 - e^{ - t / \tau})
• Match the voltage or current behavior with its corresponding equation:

  Voltage during charging ↔️ V_C(t) = V_in(1 - e^-t/τ)

  Current during charging ↔️ I(t) = (V_in/R)e^-t/τ
• In the charging equation, $\tau$ represents the time constant.
• Match the time with the approximate voltage and current values during charging:

  0τ ↔️ V_C = 0, I = V_in/R

  1τ ↔️ V_C = 63.2% of V_in, I = 36.8% of V_in/R

  2τ ↔️ V_C = 86.5% of V_in, I = 13.5% of V_in/R

  3τ ↔️ V_C = 95.0% of V_in, I = 5% of V_in/R
• What is the equation for the voltage across a capacitor during discharging?

  $V_{C}(t) =$$V_{0}e^{ - t / \tau}$
• During discharging, a larger time constant results in a slower discharge.
• The initial voltage across the capacitor during discharging is denoted as V₀.

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

  True
• What is the voltage across the capacitor at time t = 3τ during discharging?

  5% of V₀
• The current during discharging is described by the equation $I(t) =$$- \frac{V_{0}}{R} e^{ - t / \tau}$, where R represents the resistance
• Both voltage and current decrease exponentially during the discharge of an RC circuit.


  True
• During discharge, the initial voltage across the capacitor is denoted as V₀
• A larger universal time constant indicates a slower charging or discharging process.


  True
• The larger the time constant τ, the faster the capacitor discharges.

  False
• The universal time constant is calculated as \tau = RC
• 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