Concept explainers
Electric Circuits An electric circuit contains a battery that produces a voltage of 60 volts (V), a resistor with a resistance of 13 ohms (Ω), and an inductor with an inductance of 5 henrys (H), as shown in the figure on the following page. Using calculus, it can be shown that the current I = I(t) (in amperes, A) t seconds after the switch is closed is
- (a) Use this equation to express the time t as a function of the current I.
- (b) After how many seconds is the current 2 A?
(a).
To express: The value of time
Answer to Problem 87E
The value of time
Explanation of Solution
Given:
Equation of current
Calculation:
Simply the equation (1),
Take exponential of both sides of above equation to evaluate
Hence, time t as a function of I is
(b).
To Find: The time when current is 2A.
Answer to Problem 87E
The value of time
Explanation of Solution
From part (a) equation of current is,
Substitute 2 for
Hence, value of temperature T is 0.218 seconds.
Chapter 4 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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