Уровень. 1. An LC circuit consists of a 10 μF capacitor and a 0,01 mH inductor

1. An LC circuit consists of a 10 μF capacitor and a 0,01 mH inductor. What is the maximum value of charge in the capacitor, if the maximum current through the inductor is 2 mA?

2. A 100 μF capacitor is charged up to a potential difference of 10V and connected in parallel to a 0,1 mH inductor to set up electromagnetic oscillations. What is the current through the circuit when the instantaneous value of potential difference across the inductor is 4V?

3. A 10 μF capacitor is charged up to a 50 V potential difference and then connected to a 0,1 H inductor. What is the energy stored in the capacitor at t = 10^–3π s after the capacitor starts to discharge?

4. An LC circuit consists of a 20 μF capacitor and a 0,2 H inductor. The maximum charge on the capacitor is 8 mC.

a) What is the total EM energy in the circuit?

b) What is the ratio of instantaneous energy of the capacitor to that of the inductor when the instantaneous charge in the capacitor is 2 mC?

5. An LC circuit consists of a 2 μF capacitor and an 0,8 mH inductor. The maximum value of current through the inductor is 100 mA.

a) What is the maximum value of energy stored in the capacitor?

b) What is the charge in the capacitor when the instantaneous current through the inductor is 10 mA?

6. A 1 μF capacitor is charged up to a 100V potential and is then placed in parallel to an inductor of inductance L = 4H. Express charge and potential difference as functions of time.

7. The maximum values of charge and current are measured as q_m = 10^-6 C and I_m = 2mA in an ideal LC circuit. Find the frequency of oscillations.

8. Write down the effective, instantaneous and maximum values of the potential difference and current for AC circuits?

9. A sinusoidal voltage U = 100 Sin(200t – π/3) is applied to a circuit having an impedance of 5∙√2 Ω find:

a) The effective current.

b) The frequency.

c) The phase angle.

10. An alternating current is induced in a loop of 200 turns and area 400 cm² which rotates in a magnetic field of magnitude 2∙10^–2 T. Determine the instantaneous emf at t = 0,01 s after the beginning of the rotation if the amplitude of emf is 20 V.

11. A circuit having a resistor of 50 Ω is connected to an ac generator whose maximum emf is 200 V. If the frequency is 50 s^–1, what is the equation for alternating current.

12. An alternating current source having a maximum voltage value of U_m = 22 V and a frequency of 50 Hz is connected to a resistor of 22 Ω.

a) Find the maximum current of the circuit,

b) Write an expression for voltage and current at a time, t.

13. A resistor is connected to an ac source having a frequency of 100 Hz, and maximum potential difference of 170 V. To produce a maximum current through the circuit of 1,7 A, what must the value of the resistance be?

14. The voltage of an AC generator is given by u = 100 sin ωt, and the frequency of the generator is 20 s^–1, find:

a) the rms current (i_rms) in the circuit when this generator is connected to a 25 Ω resistor.

b) Instantaneous voltage and current at t = 3,004 s.

15. An AC source of voltage, u = 500 sin 100πt is connected to a resistor of R = 250 Ω. Determine:

a) The equation for instantaneous current as a function of time.

b) Effective voltage and current.

c) Frequency and angular frequency.

d) The voltage across the resistor and the current through the resistor at t = 0,5 s.

16. An inductor of L = 5 H is connected to an AC source of voltage u = 150∙sin 10πt. Write down the equation for current as a function of time. (Take π = 3)

17. Determine the maximum and rms current passing through a capacitor of 18μF, that is connected to an AC source of u _rms = 50 V and frequency 50 Hz. (Take π = 3)

18. An inductor of L = 5 mH is connected to an alternating current source having a maximum voltage of 6.4 V. Find the inductive reactance of the inductor and the maximum current when ω = 320 rad/s.

19. An alternating current having a frequency of 50 s^–1 passes through a capacitor of capacitive reactance 10/π Ω. Find the capacity of the capacitor in units of Farad (F).

20. A 50/π μF capacitor is connected to an alternatingcurrent source of 150 V. If the frequency of the source is 2 mHz, find the capacitive reactance of the capacitor and the maximum current.

21. A current of 2 A passes through a coil having an ohmic resistance of 40 Ω, when it is connected to a 100 V ac(rms) source. If the frequency of the current is 50/π s^–1, find the inductance of the coil in units of Henry (H).

22. The capacitive reactance of a capacitor is 2∙10³ Ω and is connected to a source of frequency 50 s^–1. Find the capacitance of the capacitor in μF. (Take π =3)

23. Find the resistance of a 2/π μF capacitor when the frequency of the alternating current source is.

a) 50 Hz

b) 100 Hz

24. If L = 2 H and the inductive reactance of an inductor is 628 Ω, find the frequency of the alternating current.

25. A short-wave radio transmitter generates radio waves in the short wave range, λ = 10 – 100 m. What is the frequency range of this transmitter?