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What is the time constant of the capacitor and resistor circuit? Switch closes at 1=0 s. R=1K N ww V=12V C=2000 micro-farad

What is the time constant of the capacitor and resistor circuit? Switch closes at 1=0 s. R=1K N ww V=12V C=2000 micro-farad

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The image displays a list of options with radio buttons for selecting a time interval. The options are as follows: - 1 sec - 5 sec - 10 sec - 20 sec The layout is simple, with each option positioned vertically, and a circular radio button to the left of each time interval, allowing users to select one option from the list.
Transcribed Image Text:The image displays a list of options with radio buttons for selecting a time interval. The options are as follows: - 1 sec - 5 sec - 10 sec - 20 sec The layout is simple, with each option positioned vertically, and a circular radio button to the left of each time interval, allowing users to select one option from the list.
**Transcription for Educational Website:** **Question:** What is the time constant of the capacitor and resistor circuit? **Diagram Explanation:** The diagram shows a simple RC (Resistor-Capacitor) circuit. - **Voltage Source (V):** 12V - **Resistor (R):** 1 kilo-ohm (1K Ω) - **Capacitor (C):** 2000 micro-farad (µF) - **Switch:** The switch is shown open and will close at \( t = 0 \) seconds. **Explanation of Time Constant:** The time constant (\( \tau \)) of an RC circuit is calculated using the formula: \[ \tau = R \times C \] In this context: - \( R = 1K \, \Omega = 1000 \, \Omega \) - \( C = 2000 \, \mu F = 2000 \times 10^{-6} \, F \) Therefore, \[ \tau = 1000 \times 2000 \times 10^{-6} = 2 \, \text{seconds} \] This time constant represents the time it takes for the voltage across the capacitor to reach approximately 63.2% of its final value after the switch is closed.
Transcribed Image Text:**Transcription for Educational Website:** **Question:** What is the time constant of the capacitor and resistor circuit? **Diagram Explanation:** The diagram shows a simple RC (Resistor-Capacitor) circuit. - **Voltage Source (V):** 12V - **Resistor (R):** 1 kilo-ohm (1K Ω) - **Capacitor (C):** 2000 micro-farad (µF) - **Switch:** The switch is shown open and will close at \( t = 0 \) seconds. **Explanation of Time Constant:** The time constant (\( \tau \)) of an RC circuit is calculated using the formula: \[ \tau = R \times C \] In this context: - \( R = 1K \, \Omega = 1000 \, \Omega \) - \( C = 2000 \, \mu F = 2000 \times 10^{-6} \, F \) Therefore, \[ \tau = 1000 \times 2000 \times 10^{-6} = 2 \, \text{seconds} \] This time constant represents the time it takes for the voltage across the capacitor to reach approximately 63.2% of its final value after the switch is closed.
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