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Consider the circuit below. The capacitor has 36 pF capacitance. R1 has 143 k2 of resistance and R2 has 261 k Q of resistance. The battery outputs 20 V. The switch has been in the closed position for a long time (long enough to fully charge the capacitor). At t = 0 s, the switch is opened (in the image below, the switch is open). Calculate the charge on the positive capacitor plate at t = 3,492 ns, in %3D units of pC. S2 R2 R1 C1 V1+

Consider the circuit below. The capacitor has 36 pF capacitance. R1 has 143 k2 of resistance and R2 has 261 k Q of resistance. The battery outputs 20 V. The switch has been in the closed position for a long time (long enough to fully charge the capacitor). At t = 0 s, the switch is opened (in the image below, the switch is open). Calculate the charge on the positive capacitor plate at t = 3,492 ns, in %3D units of pC. S2 R2 R1 C1 V1+

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(Please answer to the fourth decimal place - i.e 14.3225)

**Understanding Charging and Discharging of a Capacitor in an RC Circuit** Consider the circuit below. The capacitor has a capacitance of \(36 \, \text{pF}\). Resistor \(R1\) has a resistance of \(143 \, \text{k}\Omega\) and resistor \(R2\) has a resistance of \(261 \, \text{k}\Omega\). The battery provides a voltage of \(20 \, \text{V}\). The switch has been in the closed position for a long time (long enough to fully charge the capacitor). At \(t = 0 \, \text{s}\), the switch is opened (in the image below, the switch is open). Calculate the charge on the positive capacitor plate at \(t = 3,492 \, \text{ns}\), in units of picocoulombs (pC). ### Detailed Analysis of the Circuit Diagram: **Components:** - **Resistor \(R1\):** 143 \(k\Omega\) - **Resistor \(R2\):** 261 \(k\Omega\) - **Capacitor \(C1\):** 36 \(pF\) - **Battery \(V1\):** 20 \(V\) - **Switch \(S2\)** **Circuit Description:** 1. **Initial State:** The switch is closed for a long time, allowing the capacitor \(C1\) to be fully charged. 2. **At \(t = 0 \, \text{s}\):** The switch is opened, initializing the discharging process of the capacitor. ### Steps to Calculate the Charge on the Capacitor: 1. **Fully Charged Capacitor:** - Voltage across the capacitor, \( V_C = 20 \, \text{V} \). - Charge on the capacitor, \( Q_0 = C \times V = 36 \, \text{pF} \times 20 \, \text{V} = 720 \, \text{pC} \). 2. **Discharging Process:** - The time constant \( \tau \) for the circuit is given by \( \tau = R_{\text{eq}} \times C \), where \( R_{\text{eq}} \) is the equivalent resistance seen by the capacitor. - Since \( R1 \) and \( R
Transcribed Image Text:**Understanding Charging and Discharging of a Capacitor in an RC Circuit** Consider the circuit below. The capacitor has a capacitance of \(36 \, \text{pF}\). Resistor \(R1\) has a resistance of \(143 \, \text{k}\Omega\) and resistor \(R2\) has a resistance of \(261 \, \text{k}\Omega\). The battery provides a voltage of \(20 \, \text{V}\). The switch has been in the closed position for a long time (long enough to fully charge the capacitor). At \(t = 0 \, \text{s}\), the switch is opened (in the image below, the switch is open). Calculate the charge on the positive capacitor plate at \(t = 3,492 \, \text{ns}\), in units of picocoulombs (pC). ### Detailed Analysis of the Circuit Diagram: **Components:** - **Resistor \(R1\):** 143 \(k\Omega\) - **Resistor \(R2\):** 261 \(k\Omega\) - **Capacitor \(C1\):** 36 \(pF\) - **Battery \(V1\):** 20 \(V\) - **Switch \(S2\)** **Circuit Description:** 1. **Initial State:** The switch is closed for a long time, allowing the capacitor \(C1\) to be fully charged. 2. **At \(t = 0 \, \text{s}\):** The switch is opened, initializing the discharging process of the capacitor. ### Steps to Calculate the Charge on the Capacitor: 1. **Fully Charged Capacitor:** - Voltage across the capacitor, \( V_C = 20 \, \text{V} \). - Charge on the capacitor, \( Q_0 = C \times V = 36 \, \text{pF} \times 20 \, \text{V} = 720 \, \text{pC} \). 2. **Discharging Process:** - The time constant \( \tau \) for the circuit is given by \( \tau = R_{\text{eq}} \times C \), where \( R_{\text{eq}} \) is the equivalent resistance seen by the capacitor. - Since \( R1 \) and \( R
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