Electromagnetic oscillator
1. State the composition and properties of an electromagnetic oscillator.
Solution:
An electromagnetic oscillator is an alternating-current circuit with a coil (inductance) and a capacitor (capacitance). It is also called an oscillating circuit or an LC circuit. In an oscillating circuit, electrical energy is periodically converted into magnetic energy and back. Electromagnetic oscillations arise in the oscillating circuit. For the frequency of the electromagnetic oscillator (the oscillator’s natural frequency), Thomson’s relation applies:
2. How will the oscillation frequency of the LC circuit change if we move the plates of the capacitor closer together?
Solution:
If we move the plates of the capacitor in the oscillating circuit closer together, d decreases, C increases, and the frequency f decreases.
3.The oscillating circuits have parameters:
Which circuit oscillates at the higher frequency?
Solution:
Analysis:
Both LC circuits oscillate at the same frequency, f1 = f2 = 6.3 MHz.
4.An oscillating circuit consists of a capacitor with capacitance C = 10 μF and a coil with variable inductance. Over what interval must the coil’s inductance vary so that the circuit’s natural oscillation frequency varies from 400 Hz to 500 Hz?
Solution:
Analysis:
The inductance of the coil must vary from L1 = 16 mH to L2 = 10 mH.
5.The oscillating circuit consists of a coil with inductance L = 3 mH and a parallel-plate capacitor whose plates are disks of radius 1.2 cm. The separation of the plates is 0.3 mm. Determine the period of the oscillating circuit. How does the period change if we insert a dielectric with εr = 4 between the plates of the capacitor?
Solution:
Analysis:
If we insert a dielectric with εr = 4 between the plates of the capacitor, the period of the circuit doubles.
6.We connect a capacitor with capacitance C1 to a coil with constant inductance L. We find that the oscillator oscillates with natural frequency f1 = 100 kHz. If we connect a capacitor with capacitance C2 to this coil, the oscillator will oscillate with natural frequency f2 = 160 kHz. What natural frequency will the oscillator have if we connect both capacitors to the coil
- a) in parallel
- b) in series
Solution:
Analysis:
f1 = 100 kHz = 105 s-1, f2 = 160 kHz = 1.6×105 s-1
