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Problem 26.44 10 of 18 Constants I Periodic Table In the figure, the total resistance is 13.0 kN , and the battery's emf is 30.0 V. f the time constant is measured to be 27.8 us . (Figure 1) Part A Calculate the total capacitance of the circuit. ? Figure < 1 of 1> C = F R Submit Request Answer Part B Calculate the time it takes for the voltage across the resistor to reach 17.4 V after the switch is closed. nνα ΑΣφ

Problem 26.44 10 of 18 Constants I Periodic Table In the figure, the total resistance is 13.0 kN , and the battery's emf is 30.0 V. f the time constant is measured to be 27.8 us . (Figure 1) Part A Calculate the total capacitance of the circuit. ? Figure < 1 of 1> C = F R Submit Request Answer Part B Calculate the time it takes for the voltage across the resistor to reach 17.4 V after the switch is closed. nνα ΑΣφ

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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Please help me with both parts of this problem, and double check your answers, i have had many issues with tutors in the past giving incorrect answers, and thats of no use to me then

### Problem 26.44 In the figure, the total resistance is \(13.0 \, k\Omega\), and the battery's emf is \(30.0 \, V\). If the time constant is measured to be \(27.8 \, \mu s\). #### Figure The figure shows a simple RC circuit consisting of a resistor \(R\), a capacitor \(C\), a battery \(\epsilon\), and a switch \(S\). The resistor \(R\) and the capacitor \(C\) are connected in series with the battery and the switch. ![RC Circuit Diagram](https://example.edu/image.jpg) #### Part A **Problem Statement:** Calculate the total capacitance of the circuit: \[ \tau = RC \] Given: - Total resistance, \(R = 13.0 \, k\Omega\) - Time constant, \(\tau = 27.8 \, \mu s\) \[ C = \frac{\tau}{R} \] **Input Box for Answer:** \[ C = \boxed{ \text{your answer here} } \, F \] [Submit Button] #### Part B **Problem Statement:** Calculate the time it takes for the voltage across the resistor to reach \(17.4 \, V\) after the switch is closed. The voltage across the resistor in an RC circuit as a function of time \(t\) can be given by: \[ V_R(t) = V_0 (1 - e^{-t/RC}) \] Given: - Initial voltage, \(V_0 = 30.0 \, V\) - Desired voltage across the resistor, \(V_R(t) = 17.4 \, V\) - Total resistance, \(R = 13.0 \, k\Omega\) - Total capacitance \(C\) (calculated in Part A) Solve for time \(t\): \[ 17.4 = 30.0 (1 - e^{-t/RC}) \] **Input Box for Answer:** \[ t = \boxed{ \text{your answer here} } \, s \] [Submit Button]
Transcribed Image Text:### Problem 26.44 In the figure, the total resistance is \(13.0 \, k\Omega\), and the battery's emf is \(30.0 \, V\). If the time constant is measured to be \(27.8 \, \mu s\). #### Figure The figure shows a simple RC circuit consisting of a resistor \(R\), a capacitor \(C\), a battery \(\epsilon\), and a switch \(S\). The resistor \(R\) and the capacitor \(C\) are connected in series with the battery and the switch. ![RC Circuit Diagram](https://example.edu/image.jpg) #### Part A **Problem Statement:** Calculate the total capacitance of the circuit: \[ \tau = RC \] Given: - Total resistance, \(R = 13.0 \, k\Omega\) - Time constant, \(\tau = 27.8 \, \mu s\) \[ C = \frac{\tau}{R} \] **Input Box for Answer:** \[ C = \boxed{ \text{your answer here} } \, F \] [Submit Button] #### Part B **Problem Statement:** Calculate the time it takes for the voltage across the resistor to reach \(17.4 \, V\) after the switch is closed. The voltage across the resistor in an RC circuit as a function of time \(t\) can be given by: \[ V_R(t) = V_0 (1 - e^{-t/RC}) \] Given: - Initial voltage, \(V_0 = 30.0 \, V\) - Desired voltage across the resistor, \(V_R(t) = 17.4 \, V\) - Total resistance, \(R = 13.0 \, k\Omega\) - Total capacitance \(C\) (calculated in Part A) Solve for time \(t\): \[ 17.4 = 30.0 (1 - e^{-t/RC}) \] **Input Box for Answer:** \[ t = \boxed{ \text{your answer here} } \, s \] [Submit Button]
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