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A 37 µF capacitor is connected across a programmed power supply. During the interval from t = 0 to t= 5.00 s the output voltage of the supply is given by V(t) = 6.00 +4.00t - 2.00t² volts. At t = 0.600 s find (a) the charge on the capacitor, (b) the current into the capacitor, and (c) the power output from the power supply. (a) Number i (b) Number i (c) Number ! Units C Units A Units W î

A 37 µF capacitor is connected across a programmed power supply. During the interval from t = 0 to t= 5.00 s the output voltage of the supply is given by V(t) = 6.00 +4.00t - 2.00t² volts. At t = 0.600 s find (a) the charge on the capacitor, (b) the current into the capacitor, and (c) the power output from the power supply. (a) Number i (b) Number i (c) Number ! Units C Units A Units W î

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
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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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Here is the transcription and explanation of the content suitable for an educational website: --- **Problem Statement:** A 37 µF capacitor is connected across a programmed power supply. During the interval from \( t = 0 \) to \( t = 5.00 \) s, the output voltage of the supply is given by the equation \( V(t) = 6.00 + 4.00t - 2.00t^2 \) volts. At \( t = 0.600 \) s, determine the following: (a) The charge on the capacitor. (b) The current into the capacitor. (c) The power output from the power supply. **Input Fields and Units:** - For question (a), enter the number. The unit provided is Coulombs (C). - For question (b), enter the number. The unit provided is Amperes (A). - For question (c), enter the number. The unit provided is Watts (W). **Instructions for Solution:** 1. **Charge on the Capacitor (a):** - Use the formula \( q = C \times V \) to find the charge, where \( C \) is the capacitance and \( V \) is the voltage at \( t = 0.600 \) s. 2. **Current into the Capacitor (b):** - Use the relationship \( i(t) = \frac{dq}{dt} \) and consider the given voltage function to find \( i(t) \). 3. **Power Output from the Power Supply (c):** - Use the formula \( P = V(t) \times i(t) \) to calculate the power output at the given time. This setup will prompt students to apply their knowledge of capacitors, calculus, and basic electrical principles to solve practical problems using the given information.
Transcribed Image Text:Here is the transcription and explanation of the content suitable for an educational website: --- **Problem Statement:** A 37 µF capacitor is connected across a programmed power supply. During the interval from \( t = 0 \) to \( t = 5.00 \) s, the output voltage of the supply is given by the equation \( V(t) = 6.00 + 4.00t - 2.00t^2 \) volts. At \( t = 0.600 \) s, determine the following: (a) The charge on the capacitor. (b) The current into the capacitor. (c) The power output from the power supply. **Input Fields and Units:** - For question (a), enter the number. The unit provided is Coulombs (C). - For question (b), enter the number. The unit provided is Amperes (A). - For question (c), enter the number. The unit provided is Watts (W). **Instructions for Solution:** 1. **Charge on the Capacitor (a):** - Use the formula \( q = C \times V \) to find the charge, where \( C \) is the capacitance and \( V \) is the voltage at \( t = 0.600 \) s. 2. **Current into the Capacitor (b):** - Use the relationship \( i(t) = \frac{dq}{dt} \) and consider the given voltage function to find \( i(t) \). 3. **Power Output from the Power Supply (c):** - Use the formula \( P = V(t) \times i(t) \) to calculate the power output at the given time. This setup will prompt students to apply their knowledge of capacitors, calculus, and basic electrical principles to solve practical problems using the given information.
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