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Individual tasks for PROBLEM 3.4.
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DRIVEN ELECTROMAGNETIC OSCILLATIONS.
In accordance with your variant to solve one of the following problems listed below (The number of problem statement and all necessary input data are reduced in the table 3.4).
1 Simple harmonic external EMF applied to the series oscillatory circuit of RLC -filter. Three nominal values of elements of filter and one equation of current or voltage oscillations in circuit are listed in the table 3.4. We used the following notations of quantities: ε – external EMF, i – public current in circuit, uR – voltage on resistor, uC – voltage on capacitor, uL – voltage on inductor.
1) To rebuild five equations of all five electric oscillatory quantities in circuit with numerical coefficients.
2) To build the vector voltage diagram at t= 0.
3) To find the values of external EMF – ε, voltages – uR, uC, uL at the moment of time of t 1 = Т / 4 (Т – period of oscillations). To build the vector voltage diagram at t1 = Т / 4.
2 Simple harmonic external EMF on the resonance frequency applied to the series oscillatory circuit of RLC -filter. Three nominal values of elements of filter and equation of current or voltage oscillations in circuit are listed in the table 3.4. We used the following notations of quantities: ε – external EMF, i – current in circuit, uR – voltage on resistor, uC – voltage on capacitor, uL – voltage on inductor.
1) To rebuild the equation of oscillations of all five quantities in circuit with numerical coefficients.
2) To build the vector voltage diagram at t= 0.
3) To find the values of external EMF – ε, voltages – uR, uC, uL at the moment of time of t 1 = Т / 8 (Т – period of oscillations). To build the vector voltage diagram at t 1 = Т / 8.
TABLE OF TASK VARIANTS
Table 3.4
| Variant | Statement | С, mcF | L, mH | R, Ω | The equation of oscillations |
| i (t) = 0, 6× cos (2·104× t), А | |||||
| uR(t)= 6× cos (500 × t), V | |||||
| 12, 5 | ε (t)= 20× cos (Ω R× t), V | ||||
| 0, 4 | 0, 5 | uL(t)= 5× cos (5·104 × t), V | |||
| 1, 5 | ε (t)= 39, 5× cos (2·104 × t), V | ||||
| 0, 1 | i(t)= 1, 5× cos (Ω R× t), А | ||||
| 0, 05 | 7, 5 | uC(t)= 5× cos (2·105 × t), V | |||
| 0, 5 | 0, 2 | uR(t)= 15× cos (Ω R× t), V | |||
| 0, 2 | i(t)= 1, 6× cos (2, 5·104 × t), А | ||||
| 0, 5 | 0, 15 | uL(t)= 12× cos (2·105 × t), V | |||
| uR(t)= 30× cos (103 × t), V | |||||
| 7, 5 | uC(t)= 20× cos (104 × t), V | ||||
| ε (t)= 19, 3× cos (103 × t), V | |||||
| 2, 5 | uL(t)= 50× cos (Ω R× t), V | ||||
| 0, 5 | 0, 2 | i(t)= 0, 6× cos (2·105 × t), А | |||
| 0, 5 | 0, 05 | uC(t)= 30× cos (Ω R× t), V | |||
| uR(t)= 6× cos (2, 5·103 × t), V | |||||
| 0, 2 | 1, 5 | uC(t)= 25× cos (105 × t), V | |||
| ε (t)= 4, 5× cos (Ω R× t), V | |||||
| uL(t)= 20× cos (104 × t), V | |||||
| 0, 1 | ε (t)= 21, 2× cos (5·104 × t), V | ||||
| i(t)= 2× cos (Ω R× t), А | |||||
| 0, 25 | 1, 5 | uR(t)= 24× cos (4·104 × t), V | |||
| uL(t)= 3× cos (5·103 × t), V | |||||
| 0, 1 | 0, 01 | uR(t)= 6× cos (Ω R × t), V | |||
| uC(t)= 20× cos (4·103 × t), V | |||||
| 2, 5 | 2, 5 | ε (t)= 29, 7× cos (8·103 × t), V | |||
| 0, 5 | 0, 8 | uL(t)= 40× cos (Ω R× t), V | |||
| i(t)= 0, 8× cos (2·104 × t), А | |||||
| 0, 02 | 0, 05 | uC(t)= 25× cos (Ω R× t), V |
Problem 3.6.
ELECTROMAGNETIC WAVES (EMW).
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