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

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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

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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

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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.).