College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Hello, I need help with part A and part B and Part C is there any chance you can help me with those problems and also can you label them as well thank you

**Problem 2**: The switch in Fig. 2 closes at \( t = 0 \) s and, after a very long time, the capacitor is fully charged. Find expressions for the total energy supplied by the battery as the capacitor is being charged, total energy dissipated by the resistor as the capacitor is being charged, and the energy stored in the capacitor when it is fully charged. **Diagram Explanation**: - The diagram (Fig. 2) shows a simple RC circuit with a battery of EMF \( \mathcal{E} \), a resistor \( R \), and a capacitor \( C \). **Questions and Explanations**: **a)** In an ideal battery, a charge \( dq \) gains potential energy \( \mathcal{E} dq \) as it moves up the 'charge escalator' inside the battery. Therefore, the power supplied by the battery at each moment of time is \( P_{\text{bat}} = \frac{dq}{dt} \mathcal{E} = I \mathcal{E} \) (this expression was derived in paragraph 28.3 of the textbook). The current in an RC circuit with a charging capacitor changes with time as \( I = I_0 e^{-t/ \tau} \), where \( I_0 = \frac{\mathcal{E}}{R} \) and \( \tau = RC \) (this expression was provided at the end of paragraph 28.9 of the textbook). To compute the total energy supplied by the battery as the capacitor is charging, take the integral \( E_{\text{bat}} = \int_{t=0}^{\infty} P_{\text{bat}} dt \). Express the final answer for \( E_{\text{bat}} \) in terms of \( \mathcal{E} \) and \( C \) only. **b)** The power dissipated by the resistor is equal to \( P_{\text{res}} = I^2 R \) (note that it is a function of time in this problem). Compute the total energy dissipated in the resistor by taking the integral \( E_{\text{res}} = \int_{t=0}^{\infty} P_{\text{res}} dt \). Express your answer in terms of \( \mathcal{E} \) and \( C \) only. **c)** When the capacitor is
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Transcribed Image Text:**Problem 2**: The switch in Fig. 2 closes at \( t = 0 \) s and, after a very long time, the capacitor is fully charged. Find expressions for the total energy supplied by the battery as the capacitor is being charged, total energy dissipated by the resistor as the capacitor is being charged, and the energy stored in the capacitor when it is fully charged. **Diagram Explanation**: - The diagram (Fig. 2) shows a simple RC circuit with a battery of EMF \( \mathcal{E} \), a resistor \( R \), and a capacitor \( C \). **Questions and Explanations**: **a)** In an ideal battery, a charge \( dq \) gains potential energy \( \mathcal{E} dq \) as it moves up the 'charge escalator' inside the battery. Therefore, the power supplied by the battery at each moment of time is \( P_{\text{bat}} = \frac{dq}{dt} \mathcal{E} = I \mathcal{E} \) (this expression was derived in paragraph 28.3 of the textbook). The current in an RC circuit with a charging capacitor changes with time as \( I = I_0 e^{-t/ \tau} \), where \( I_0 = \frac{\mathcal{E}}{R} \) and \( \tau = RC \) (this expression was provided at the end of paragraph 28.9 of the textbook). To compute the total energy supplied by the battery as the capacitor is charging, take the integral \( E_{\text{bat}} = \int_{t=0}^{\infty} P_{\text{bat}} dt \). Express the final answer for \( E_{\text{bat}} \) in terms of \( \mathcal{E} \) and \( C \) only. **b)** The power dissipated by the resistor is equal to \( P_{\text{res}} = I^2 R \) (note that it is a function of time in this problem). Compute the total energy dissipated in the resistor by taking the integral \( E_{\text{res}} = \int_{t=0}^{\infty} P_{\text{res}} dt \). Express your answer in terms of \( \mathcal{E} \) and \( C \) only. **c)** When the capacitor is
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