Concept explainers
Charging a Capacitor See the illustration. If a charged capacitor is connected to a coil by closing a switch, energy is transferred to the coil and then back to the capacitor in an oscillatory motion. The voltage (in volts) across the capacitor will gradually diminish to 0 with time (in seconds).
(a) Graph the function relating :
(b) At what times will the graph of touch the graph of ? When does the graph of touch the graph of ?
(c) When will the voltage be between volt?
a. Graph the function relating and :
b. At what times will the graph of touch the graph
When does the graph of touch the graph of
c. When will the voltage be between and volt?
Answer to Problem 55AYU
a. The graph is plotted.
b. The graph of touches the graph of when , 2. The touches when
c. when and
Explanation of Solution
Given:
If a charged capacitor is connected to a coil by closing a switch, energy is transferred to the coil and then back to the capacitor in an oscillatory motion. The voltage (in volts) across the capacitor will gradually diminish to 0 with time (in seconds).
Calculation:
a. Graph of
b. On the interval , the graph of touches the graph of when , 2. The touches when
c. From the graph we see that at various intervals.
When
and
Chapter 8 Solutions
Precalculus
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