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6.15 The current and voltage for a 0.6 µF capacitor are both zero for t < 0. For t≥ 0, the current is 3 cos 50,000t A. a) Find the expression for the voltage drop across the capacitor in the direction of the current. b) Find the maximum power delivered to the capacitor any one instant in time. c) Find the maximum energy stored in the capaci- tor any one instant in time.

6.15 The current and voltage for a 0.6 µF capacitor are both zero for t < 0. For t≥ 0, the current is 3 cos 50,000t A. a) Find the expression for the voltage drop across the capacitor in the direction of the current. b) Find the maximum power delivered to the capacitor any one instant in time. c) Find the maximum energy stored in the capaci- tor any one instant in time.

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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Circuits 1 HW 5 Q6
### Problem 6.15 The problem involves a 0.6 μF capacitor, where both current and voltage are zero for \( t < 0 \). For \( t \geq 0 \), the current is given by: \[ I(t) = 3 \cos(50,000t) \, \text{A} \] #### Tasks a) **Find the expression for the voltage drop across the capacitor in the direction of the current.** b) **Find the maximum power delivered to the capacitor at any instant in time.** c) **Find the maximum energy stored in the capacitor at any instant in time.** ### Explanation This problem involves analyzing a capacitor in an AC circuit with the given current function. Calculations involve: - Using the relation \( V(t) = \frac{1}{C} \int I(t) \, dt \) to find the voltage across the capacitor. - Using the power formula \( P(t) = V(t) \cdot I(t) \) to find the maximum power. - Using the energy formula \( W = \frac{1}{2} C V(t)^2 \) to determine the energy stored.
Transcribed Image Text:### Problem 6.15 The problem involves a 0.6 μF capacitor, where both current and voltage are zero for \( t < 0 \). For \( t \geq 0 \), the current is given by: \[ I(t) = 3 \cos(50,000t) \, \text{A} \] #### Tasks a) **Find the expression for the voltage drop across the capacitor in the direction of the current.** b) **Find the maximum power delivered to the capacitor at any instant in time.** c) **Find the maximum energy stored in the capacitor at any instant in time.** ### Explanation This problem involves analyzing a capacitor in an AC circuit with the given current function. Calculations involve: - Using the relation \( V(t) = \frac{1}{C} \int I(t) \, dt \) to find the voltage across the capacitor. - Using the power formula \( P(t) = V(t) \cdot I(t) \) to find the maximum power. - Using the energy formula \( W = \frac{1}{2} C V(t)^2 \) to determine the energy stored.
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