Question
In Exercises $29-44,$ solve the given problems by using implicit differentiation.In an RLC circuit, the angular frequency $\omega$ at which the circuit resonates is given by $\omega^{2}=1 / L C-R^{2} / L^{2} .$ Find $d \omega / d L.$
Step 1
This gives us: $$2\omega \frac{d\omega}{dL} = -\frac{1}{LC^{2}} + \frac{2R^{2}}{L^{3}}$$ Show more…
Show all steps
Your feedback will help us improve your experience
Willis James and 87 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A series circuit containing inductance $L_{1}$ and capacitance $C_{1}$ oscillates at angular frequency $\omega .$ A second series circuit, containing inductance $L_{2}$ and capacitance $C_{2},$ oscillates at the same angular frequency. In terms of $\omega,$ what is the angular frequency of oscillation of a series circuit containing all four of these elements? Neglect resistance. (Hint: Use the formulas for equivalent capacitance and equivalent inductance; see Module $25-3$ and Problem 47 in Chapter 30.)
Solve the given problems. The resonant frequency $\omega$ of a capacitance $C$ in parallel with a resistance $R$ and inductance $L$ (see Fig. 11.9 ) is $$\omega=\frac{1}{\sqrt{L C}} \sqrt{1-\frac{R^{2} C}{L}}$$ Combine terms under the radical, rationalize the denominator, and simplify. (FIGURE CAN'T COPY)
Exponents and Radicals
Multiplication and Division of Radicals
Figure 2 shows a circuit with a resistor, an inductor, and a capacitor in parallel. Kirchhoff’s rules can be used to express the impedance of the system as 1/Z=√(1/R^2 +(ωC-1/ωL)^2 ) where Z = impedance (Ω) and ω = the angular frequency. Find the ω that results in an impedance of 75 Ω with initial guesses of 1 and 1000 for the following parameters: R = 225 Ω, C = 0.6 × 10-6 F, and L = 0.5 H.
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD