Solution Found!
The equation preceding Eq. (30.27) may be converted into
Chapter 30, Problem 55P(choose chapter or problem)
CALC The equation preceding Eq. (30.27) may be converted into an energy relationship. Multiply both sides of this equation by \(-i=-d q / d t\). The first term then becomes \(i^{2} R\). Show that the second term can be written as \(d\left(\frac{1}{2} L i^{2}\right) / d t\) and that the third term can be written as \(d\left(q^{2} 2 C\right) / d t\). What does the resulting equation say about energy conservation in the circuit?
Equation Transcription:
Text Transcription:
-i=-dq/dt
i^2R
d(1 over 2 Li^2)/dt
d(q^22C)/dt
Questions & Answers
QUESTION:
CALC The equation preceding Eq. (30.27) may be converted into an energy relationship. Multiply both sides of this equation by \(-i=-d q / d t\). The first term then becomes \(i^{2} R\). Show that the second term can be written as \(d\left(\frac{1}{2} L i^{2}\right) / d t\) and that the third term can be written as \(d\left(q^{2} 2 C\right) / d t\). What does the resulting equation say about energy conservation in the circuit?
Equation Transcription:
Text Transcription:
-i=-dq/dt
i^2R
d(1 over 2 Li^2)/dt
d(q^22C)/dt
ANSWER:
Solution 55P
The given equation is,
Multiplying this equation by
Now, multiplying both sides if this equation by L,
(since
)