John 123
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Using the following o.d.e
<br /> L\frac{d^2i}{dt^2}+R\frac{di}{dt}+\frac{1}{C}i=\frac{d}{dt}E(t)<br />
The following problem has several parts all of which I have solved except for the one below.
L=1/20
R=5
<br /> C=4.10^{-4}<br />
<br /> \frac{dE}{dt}=200\cos100t<br />
Where L is an inductance in henries, R is a resistance in ohms, C is a capacitance in farads and E is the emf in volts.
The part I cannot agree with the book is as follows.
Firstly:
What should the frequency of the input E(t) be in order that it be in resonance with the system? [This I have solved correctly as :
<br /> 100\sqrt5 <br />
radians/sec
But this part leads to the next which I can't agree.
What is the maximum value of the current amplitude for this resonant frequency?
Book Answer= 2/5 amp.
John
<br /> L\frac{d^2i}{dt^2}+R\frac{di}{dt}+\frac{1}{C}i=\frac{d}{dt}E(t)<br />
The following problem has several parts all of which I have solved except for the one below.
L=1/20
R=5
<br /> C=4.10^{-4}<br />
<br /> \frac{dE}{dt}=200\cos100t<br />
Where L is an inductance in henries, R is a resistance in ohms, C is a capacitance in farads and E is the emf in volts.
The part I cannot agree with the book is as follows.
Firstly:
What should the frequency of the input E(t) be in order that it be in resonance with the system? [This I have solved correctly as :
<br /> 100\sqrt5 <br />
radians/sec
But this part leads to the next which I can't agree.
What is the maximum value of the current amplitude for this resonant frequency?
Book Answer= 2/5 amp.
John
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