Differential equation based on Kirchoff's voltage law

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SUMMARY

The discussion centers on a series circuit comprising a 15mH inductor, a 35μF capacitor, and a 5-ohm resistor, driven by a sinusoidal EMF source at 500Hz. Participants confirm that the charge on the capacitor oscillates at the same frequency of 500Hz. This conclusion is derived from applying Kirchhoff's voltage law to formulate and solve the differential equation governing the circuit. The concept of forced oscillations is also introduced, emphasizing the distinction between forced and natural responses under steady-state conditions.

PREREQUISITES
  • Understanding of Kirchhoff's voltage law
  • Basic knowledge of differential equations
  • Familiarity with electrical components: inductors, capacitors, and resistors
  • Concept of forced and natural oscillations
NEXT STEPS
  • Study the derivation of differential equations in electrical circuits
  • Learn about forced oscillations in RLC circuits
  • Explore the implications of steady-state versus transient responses
  • Investigate the impact of frequency on circuit behavior
USEFUL FOR

Electrical engineers, physics students, and anyone interested in circuit analysis and the dynamics of oscillating systems will benefit from this discussion.

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a series circuit with an inductance of 15mH, a capacitance of 35*10^(-6) F and a resistance of 5 ohms conatain a sinusoidal source of emf with a frequency of 500Hz. The frequency with which the charge on the capacitor oscillates is?

i think that it should still be 500Hz, right?
 
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Yes, you are right. This can be verified by writing out the differential equation based on Kirchoff's voltage law and solving for the current or voltage across the capacitor.

These are known as forced oscillations. Suppose you have a physical spring. If you hang a mass on it and perturb it, it will oscillate at some natural frequency. You can also of course, hold onto the mass with your hand and make it move at any frequency you desire.

Additional note: You also must assume steady state conditions. In transients you will find that there will be the forced + natural responses to a system.
 
thank you very much!
 

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