11.6 RC Circuits

• 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 effect does a higher time constant have on the charging of a capacitor?

  Slower charging
• 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 is the current equation during the discharging of an RC circuit?

  $I(t) =$$- \frac{V_{0}}{R} e^{ - t / \tau}$
• What effect does a larger time constant have on the discharge rate of a capacitor?

  It slows it down
• 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}
• 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
• What is the impact of a higher time constant on the charging rate 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
• A longer time constant indicates faster charging in an RC circuit.

  False
• The time constant $\tau$ in an RC circuit is equal to the product of resistance and capacitance
• What happens to the voltage across a capacitor during the discharging of an RC circuit?

  Decreases exponentially
• Arrange the time intervals in increasing order of the percentage of initial voltage remaining across the capacitor during discharge.

  1️⃣ 1τ

  2️⃣ 2τ

  3️⃣ 3τ

  4️⃣ 4τ
• 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
• What is the time constant in an RC circuit the time it takes for a capacitor to charge or discharge to?

  63.2% of full capacity
• The voltage equation during charging is V_{C}(t) = V_{\in}(1 - e^{ - t / \tau})
• 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
• The time constant (τ) in an RC circuit increases if either the resistance (R) or capacitance (C) increases.


  True
• The time constant (τ) has a direct relationship with both resistance (R) and capacitance (C).


  True
• 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%
• 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 time constant determines the rate of discharge in an RC circuit.


  True
• The time constant in an RC circuit increases if the resistance increases.


  True
• The voltage across a capacitor during charging is given by the equation V_{C}(t) = V_{\in}(1 - e^{ - t / \tau})
• What happens to the voltage and current in an RC circuit during charging?

  Voltage increases, current decreases
• 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
• A larger time constant in an RC circuit results in slower charging.


  True
• What is the equation for the voltage across a capacitor during discharging?

  $V_{C}(t) =$$V_{0}e^{ - t / \tau}$
• What does the time constant τ represent in an RC circuit?

  τ = RC
• The current in an RC circuit during discharging is given by the equation $I(t) =$$- \frac{V_{0}}{R} e^{ - t / \tau}$, where the negative sign indicates the direction of the current
• What is the voltage across the capacitor at time t = 3τ during discharging?

  5% of V₀