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The voltage at the terminals of the 0.6 µF capacitor shown in the figure is 0 for t < 0 and 40e-15,000t sin 30, 000t V for t≥ 0. Find (a) i(0); (b) the power delivered to the capacitor at t = 7/80 ms; and (c) the energy stored in the capacitor at t = 7/80 ms.

The voltage at the terminals of the 0.6 µF capacitor shown in the figure is 0 for t < 0 and 40e-15,000t sin 30, 000t V for t≥ 0. Find (a) i(0); (b) the power delivered to the capacitor at t = 7/80 ms; and (c) the energy stored in the capacitor at t = 7/80 ms.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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### Capacitor Voltage and Analysis Problem The voltage at the terminals of the \(0.6 \, \mu \text{F}\) capacitor shown in the figure is: \[ v(t) = \begin{cases} 0 & \text{for } t < 0 \\ 40 e^{-15,000t} \sin(30,000t) \, \text{V} & \text{for } t \geq 0 \end{cases} \] You are required to determine the following: 1. \(i(0)\) - the initial current through the capacitor at \( t = 0 \). 2. The power delivered to the capacitor at \( t = \frac{\pi}{80} \, \text{ms} \). 3. The energy stored in the capacitor at \( t = \frac{\pi}{80} \, \text{ms} \). ### Given Data: - **Capacitance:** \(0.6 \, \mu \text{F}\) - **Voltage for \( t < 0 \):** \(0 \, \text{V}\) - **Voltage for \( t \geq 0 \):** \( 40 e^{-15,000t} \sin(30,000t) \, \text{V} \) ### Diagram The circuit diagram includes: - A capacitor denoted by a standard capacitor symbol. - The capacitor is annotated with its capacitance value of \(0.6 \, \mu \text{F}\). - Voltage across the capacitor \(v\) is shown as \( v \). - Current through the capacitor \(i\) is shown as \( i \). - Polarity of the voltage and current direction are indicated by '+' and '-' signs and an arrow respectively. ### Steps to Solve: **a) Find \( i(0) \):** Use the relationship for current through a capacitor: \[ i(t) = C \frac{dv(t)}{dt} \] where \( C \) is the capacitance. **b) Find the Power Delivered to the Capacitor:** Power \(P(t)\) is given by the product of voltage and current: \[ P(t) = v(t) \cdot i(t) \] Calculate this at \( t = \frac{\pi}{80
Transcribed Image Text:### Capacitor Voltage and Analysis Problem The voltage at the terminals of the \(0.6 \, \mu \text{F}\) capacitor shown in the figure is: \[ v(t) = \begin{cases} 0 & \text{for } t < 0 \\ 40 e^{-15,000t} \sin(30,000t) \, \text{V} & \text{for } t \geq 0 \end{cases} \] You are required to determine the following: 1. \(i(0)\) - the initial current through the capacitor at \( t = 0 \). 2. The power delivered to the capacitor at \( t = \frac{\pi}{80} \, \text{ms} \). 3. The energy stored in the capacitor at \( t = \frac{\pi}{80} \, \text{ms} \). ### Given Data: - **Capacitance:** \(0.6 \, \mu \text{F}\) - **Voltage for \( t < 0 \):** \(0 \, \text{V}\) - **Voltage for \( t \geq 0 \):** \( 40 e^{-15,000t} \sin(30,000t) \, \text{V} \) ### Diagram The circuit diagram includes: - A capacitor denoted by a standard capacitor symbol. - The capacitor is annotated with its capacitance value of \(0.6 \, \mu \text{F}\). - Voltage across the capacitor \(v\) is shown as \( v \). - Current through the capacitor \(i\) is shown as \( i \). - Polarity of the voltage and current direction are indicated by '+' and '-' signs and an arrow respectively. ### Steps to Solve: **a) Find \( i(0) \):** Use the relationship for current through a capacitor: \[ i(t) = C \frac{dv(t)}{dt} \] where \( C \) is the capacitance. **b) Find the Power Delivered to the Capacitor:** Power \(P(t)\) is given by the product of voltage and current: \[ P(t) = v(t) \cdot i(t) \] Calculate this at \( t = \frac{\pi}{80
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Answer to B and C is incorrect. Please fix. 

Could you show me the correct steps and how to get the correct answer.

The correct answers are:

B: -649.2mW

C: 126.13 uJ

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