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Mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Electric Circuit Question
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Problem Number 1
If a capacitor with capacitance 7.3 farads and an inductor with inductance 5.8 henry form an oscillating circuit, then if the initial charge on the capacitor is 4.5 Coulombs and the initial current dQ/dt is 0, what function gives the charge Q as a function of clock time? The voltage across the inductor is L Q'', the voltage across the capacitor is C Q and the total voltage around the circuit is 0.
L*(d^2Q/dt^2) + Q/C = 0
(d^2)/(dt^2) + Q/(L*C) = 0
d^2Q/dt^2 + Q/(1/ 6.5) = 0
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You don't show where your 6.5 came from. However it appears that L * C = 7.3 * 5.8. The units are Henries * Farads.
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d^2Q/dt^2 + [(1/6.5)^2]*Q = 0
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Now the 6.5 is squared, so it seems that 6.5 is the square root of L * C. This would be valid.
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Q(t) = C1*cos[(1/6.5)t] + C2*sin[(1/6.5)t]
Q(0) = 4.5 = C1 * cos[(1/6.5)* 0] + C2*sin[(1/6.5) * 0]
C1 = 4.5
Q(t) = 4.5cos[(1/18)t]
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Everything you have appears to be good, but you haven't found C2. This is found from the initial condition that the initial current is zero.
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Is this the correct solution? I read the problem as Q(0) = 4.5. Can I find C2 based on the information given? Is I(0) = 0?
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Check my note just above.
I(t) is of course the derivative of Q(t).
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&#Good responses. See my notes and let me know if you have questions. &#