How Do You Solve for Inductance and Resistance in an RLC Circuit?

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The discussion focuses on solving for inductance and resistance in an RLC circuit with a given capacitance of 0.26 µF and a resonant frequency of 95 MHz. The correct inductance calculated is 10.5712 pH using the formula omega = 1/(LC)^(1/2). For determining the resistance, the impedance at resonance was initially set equal to the impedance at 10 kHz, but the user faced difficulties due to multiple unknowns. Ultimately, the user resolved their issues with math errors and successfully found the resistance value. The thread highlights the importance of correctly applying formulas and troubleshooting mathematical errors in circuit analysis.
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Homework Statement



An RLC circuit has a capacitance of C=0.26 µF.

(a) What inductance will produce a resonant frequency of 95 Mz? -----pH
(b) If the impedance at resonance is 1/5 of the impedance at 10 kHz, what value of R should be chosen? ----Ohm

Homework Equations



omega = 1/(LC)^1/2

Z=[(R^2 + (wL-(1/wC)^2]^1/2



The Attempt at a Solution



Part (a): I used omega = 1/(LC)^1/2, and got the correct answer, 10.5712pH

Part (b): I tried setting the impendane at resonance equal to the impendance at 10kHz and solving for R, but I could not arrive at a solution. So, instead, since Z=R at resonance, I tried solving the impendance equation only at resonace for Z=R, but I have too many unknowns. Can anyone offer a hint as to how I should set this part up? Thanks!
 
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Nevermind, math errors. I managed to figure it out.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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