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Chapter 8: Q39P (page 430)

Find the solutions of (1.2)(putI=dqIdt)and (1.3), if V=V0sin蝇't( const.).

Short Answer

Expert verified

Answer

The solution is Ld2ldt2+Rdldt+IC-V0蝇'cos蝇't.

Step by step solution

01

Given information from question

Given values are I=dqIdt)andV=Vusin蝇't

02

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:

Ldldt+RI+qC=V

03

The wide range of topics giving to differential equation

Given that,

V=V0sin蝇't蝇'=constant 鈥︹�︹�� (1)

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

From equation (1)

Ldtdt+RI+qC=V0sin蝇't

Differentiating this equation with respect to t and substitute dqdt=I

Ld2Idt2+RdIdt+IC=ICV0sin蝇'tLd2Idt2+RdIdt+IC=V0蝇'cos蝇't

\\

Thus, the solution is Ld2Idt2+Rdtdt+IC=V0蝇't.

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