(a) To show that I ( t ) = V R 2 + L 2 ω 2 ( R sin ω t − L ω cos ω t ) + C e − R t / L .

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Answer 1

Question

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

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Answer 2

Question

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

Expert Solution & Answer

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See solution

Answer 5

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

Answer 6

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

Answer 7

Chapter 10.5, Problem 49E

To determine

(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

Answer 8

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

Answer 9

To determine

(b)

To choose $θ$ , so that $Z \cos θ = R$ and $Z \sin θ = L ω$ ,using the addition formula for the sine function to show that

$I (t) = \frac{V}{Z} \sin (ω t - θ) + C e^{- R t / L}$ given $Z = \sqrt{R^{2} + L^{2} ω^{2}}$ . This shows that the current in the circuit varies sinusoidally apart from a DC term (called the transient current in electronics) that decreases exponentially .

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 10.1 - Prob. 1PQ Ch. 10.1 - Prob. 2PQ Ch. 10.1 - Prob. 3PQ Ch. 10.1 - Prob. 4PQ Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E

(a) To show that I ( t ) = V R 2 + L 2 ω 2 ( R sin ω t − L ω cos ω t ) + C e − R t / L .

Solution Summary: The author explains that the given equation is of linear form, so use the integrating factor to determine the solution.

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(a)

To show that $I (t) = \frac{V}{R^{2} + L^{2} ω^{2}} (R \sin ω t - L ω \cos ω t) + C e^{- R t / L}$ .

Want to see the full answer?

Chapter 10 Solutions

(a) To show that I ( t ) = V R 2 + L 2 ω 2 ( R sin ω t − L ω cos ω t ) + C e − R t / L .

Solution Summary: The author explains that the given equation is of linear form, so use the integrating factor to determine the solution.

Videos