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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
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Applications and ExamplesVoltage in a discharging

Chapter 7, Problem 28E

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QUESTION:

Problem 28E

Applications and Examples

Voltage in a discharging capacitor Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage V across its terminals and that, if t is measured in seconds,

Solve this equation for V, using V0 to denote the value of V when t = 0. How long will it take the voltage to drop to 10% of its original value?

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QUESTION:

Problem 28E

Applications and Examples

Voltage in a discharging capacitor Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage V across its terminals and that, if t is measured in seconds,

Solve this equation for V, using V0 to denote the value of V when t = 0. How long will it take the voltage to drop to 10% of its original value?

ANSWER:

SOLUTION:

Step 1 of 4:

In this question, suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage  across its terminals and that, if t is measured in seconds,

Solve this equation for , using  to denote the value of  when . Find how long will it take the voltage to drop to 10% of its original value.

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