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94 . Consider the circuit below. (a) What is the initial current through resistor ?2 when the switch is closed? (b) What is the current through resistor ?2 when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor ?1 reaches half of its initial value?

94 . Consider the circuit below. (a) What is the initial current through resistor ?2 when the switch is closed? (b) What is the current through resistor ?2 when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor ?1 reaches half of its initial value?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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94 . Consider the circuit below. (a) What is the initial current through resistor ?2 when the switch is closed? (b) What is the current through resistor ?2 when the capacitor is fully charged, long after the switch is closed? (c) What happens if the switch is opened after it has been closed for some time? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor ?1 reaches half of its initial value?

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Certainly! Here's a transcription of the handwritten notes and an explanation of the diagram, suitable for an educational website: --- ### Transcription: **Given:** \[ R_1 = 10 \times 10^3 \, \Omega \] \[ R_2 = 300 \, \Omega \] \[ C_1 = 7 \times 10^{-6} \, F \] \[ V_i = 29 \, V \] **Questions:** a) \( I(R_2, t \rightarrow 0^+) \, ? \) b) \( I(R_2, t \rightarrow \infty) \, ? \) c) \( t: I = \frac{I(t=0)}{2} \, ? \) **Steps:** 1. **At \( t = 0^- \):** \( Q = 0, \, I_2 = 0 \, A \) \( \Rightarrow I_1 = I_3 \) 2. **At \( t = 0^+ \):** \( V_i - (R_1 + R_2) I(t=0) = 0 \) \[ I_1(t=0) = \frac{V_i}{R_1 + R_2} \] 3. **At \( t = \infty \):** a) **i) \( I_1 = I_2 + I_3 \)** b) **ii) \( V_i - I_1 R_2 - I_3 R_2 = 0 \)** c) **iii) \( \Delta V_c - I_3 R_2 = 0 \Rightarrow \)** \[ \frac{Q}{C_1} - \frac{dQ/dt}{C_1} - R_1 = 0 \] \(\Rightarrow q(t) = Q_{\text{max}} e^{-t/R_1C_1}\) 4. **General Equation for Current:** \[ I(t) = I_0 \cdot e^{-t/R_1C_1} \] \[ \therefore \frac{I(t)}{I_0} = e^{-t/R_1C_1}, \ln \] \
Transcribed Image Text:Certainly! Here's a transcription of the handwritten notes and an explanation of the diagram, suitable for an educational website: --- ### Transcription: **Given:** \[ R_1 = 10 \times 10^3 \, \Omega \] \[ R_2 = 300 \, \Omega \] \[ C_1 = 7 \times 10^{-6} \, F \] \[ V_i = 29 \, V \] **Questions:** a) \( I(R_2, t \rightarrow 0^+) \, ? \) b) \( I(R_2, t \rightarrow \infty) \, ? \) c) \( t: I = \frac{I(t=0)}{2} \, ? \) **Steps:** 1. **At \( t = 0^- \):** \( Q = 0, \, I_2 = 0 \, A \) \( \Rightarrow I_1 = I_3 \) 2. **At \( t = 0^+ \):** \( V_i - (R_1 + R_2) I(t=0) = 0 \) \[ I_1(t=0) = \frac{V_i}{R_1 + R_2} \] 3. **At \( t = \infty \):** a) **i) \( I_1 = I_2 + I_3 \)** b) **ii) \( V_i - I_1 R_2 - I_3 R_2 = 0 \)** c) **iii) \( \Delta V_c - I_3 R_2 = 0 \Rightarrow \)** \[ \frac{Q}{C_1} - \frac{dQ/dt}{C_1} - R_1 = 0 \] \(\Rightarrow q(t) = Q_{\text{max}} e^{-t/R_1C_1}\) 4. **General Equation for Current:** \[ I(t) = I_0 \cdot e^{-t/R_1C_1} \] \[ \therefore \frac{I(t)}{I_0} = e^{-t/R_1C_1}, \ln \] \
The diagram illustrates an electrical circuit consisting of several components. 1. **Voltage Source (V1):** - The circuit is powered by a battery providing a voltage of \( V_1 = 24 \text{ V} \). 2. **Resistors:** - There are two resistors in the circuit: - \( R_1 = 10 \text{ k}\Omega \) - \( R_2 = 30 \text{ k}\Omega \) 3. **Capacitor (\( C_1 \)):** - A capacitor with a capacitance of \( 10 \, \mu\text{F} \) is included in the circuit. 4. **Switch:** - A switch is present in the circuit, which can be opened or closed to control the flow of current. 5. **Circuit Configuration:** - The components are arranged in a mixed series-parallel configuration. - The switch and \( R_1 \) are in series with the voltage source. - \( R_2 \) is in parallel with the capacitor \( C_1 \). The circuit can be used to study the behavior of resistors and capacitors in varying configurations, particularly observing the effects of charging and discharging in the capacitor through the resistors when the switch is operated.
Transcribed Image Text:The diagram illustrates an electrical circuit consisting of several components. 1. **Voltage Source (V1):** - The circuit is powered by a battery providing a voltage of \( V_1 = 24 \text{ V} \). 2. **Resistors:** - There are two resistors in the circuit: - \( R_1 = 10 \text{ k}\Omega \) - \( R_2 = 30 \text{ k}\Omega \) 3. **Capacitor (\( C_1 \)):** - A capacitor with a capacitance of \( 10 \, \mu\text{F} \) is included in the circuit. 4. **Switch:** - A switch is present in the circuit, which can be opened or closed to control the flow of current. 5. **Circuit Configuration:** - The components are arranged in a mixed series-parallel configuration. - The switch and \( R_1 \) are in series with the voltage source. - \( R_2 \) is in parallel with the capacitor \( C_1 \). The circuit can be used to study the behavior of resistors and capacitors in varying configurations, particularly observing the effects of charging and discharging in the capacitor through the resistors when the switch is operated.
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