Chapter 8: Q39P (page 430)

Find the solutions of (1.2) $(p u t I = d q I d t)$ and (1.3), if $V = V_{0} s i n ω' t$ ( const.).

Short Answer

Expert verified

Answer

The solution is $L \frac{d^{2} l}{d t^{2}} + R \frac{d l}{d t} + \frac{I}{C} - V_{0} ω' \cos ω' t$ .

Step by step solution

Given information from question

Given values are $I = d q I d t)$ and $V = V_{u} \sin ω' t$

The differential equation satisfied by the current in a simple series circuit

The differential equation satisfied by the current in a simple series circuit is:

$L \frac{d l}{d t} + R I + \frac{q}{C} = V$

The wide range of topics giving to differential equation

Given that,

$V = V_{0} \sin ω' t (ω' = c o n s \tan t)$ ……… (1)

The differential equation satisfied by the current in a simple series circuit is:

From equation (1)

L \frac{d t}{d t} + R I + \frac{q}{C} = V_{0} \sin ω' t

Differentiating this equation with respect to t and substitute $\frac{d q}{d t} = I$

$L \frac{d^{2} I}{d t^{2}} + R \frac{d I}{d t} + \frac{I}{C} = \frac{I}{C} (V_{0} \sin ω' t) L \frac{d^{2} I}{d t^{2}} + R \frac{d I}{d t} + \frac{I}{C} = V_{0} ω' \cos ω' t$

Thus, the solution is $L \frac{d^{2} I}{d t^{2}} + R \frac{d t}{d t} + \frac{I}{C} = V_{0} ω' t$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the solutions of (1.2) $(p u t I = d q I d t)$ and (1.3), if $V = V_{0} s i n ω' t$ ( const.).

Short Answer

Step by step solution

Given information from question

The differential equation satisfied by the current in a simple series circuit

The wide range of topics giving to differential equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Electric Charge Field and Potential

Scientific Method Physics

Fluids

Electricity

Space Physics

Study anywhere. Anytime. Across all devices.

Find the solutions of (1.2)(putI=dqIdt)and (1.3), if V=V0sinω't( const.).

Short Answer

Step by step solution

Given information from question

The differential equation satisfied by the current in a simple series circuit

The wide range of topics giving to differential equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Electric Charge Field and Potential

Scientific Method Physics

Fluids

Electricity

Space Physics

Study anywhere. Anytime. Across all devices.

Find the solutions of (1.2) $(p u t I = d q I d t)$ and (1.3), if $V = V_{0} s i n ω' t$ ( const.).