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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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Changing voltage The voltage V (volts), current I

Chapter 3, Problem 15E

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QUESTION:

Problem 15E

Changing voltage The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V = IR.Suppose that V is increasing at the rate of 1 volt sec while I is decreasing at the rate of 1 3 amp sec. Let t denote time in seconds.

a. What is the value of dV/dt?

b. What is the value of dV/dt?

c. What equation relates dR/dt to dV/dt and dI/dt?

d. Find the rate at which R is changing when V = 12 volts and I = 2 amp. Is R increasing, or decreasing?

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QUESTION:

Problem 15E

Changing voltage The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V = IR.Suppose that V is increasing at the rate of 1 volt sec while I is decreasing at the rate of 1 3 amp sec. Let t denote time in seconds.

a. What is the value of dV/dt?

b. What is the value of dV/dt?

c. What equation relates dR/dt to dV/dt and dI/dt?

d. Find the rate at which R is changing when V = 12 volts and I = 2 amp. Is R increasing, or decreasing?

ANSWER:

Solution

Step 1 of 2

Here it is given that

(a) V is increasing at that rate of 1 volt/sec

So,

.

Positive because V is increasing .

(b) I is decreasing at the rate of

So,

Negative because I is decreasing.

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