APhO 2004, Експеримент — Задача 2. Black box

Experimental Competition - Problem No. 2. Black box

Условие

APPARATUS AND MATERIALS

  1. A double beam oscilloscope.
  2. A function generator capable to generate sine, triangle and square waves over the 0.02 Hz to 2 MHz range.
  3. A "Black box" with two groups of connectors: the ABCD group and A'B'C'D' group. Besides, there are also two connectors for the standard resistor Rn=5 kΩR_\mathrm{n} = 5\ \mathrm{k\Omega}, which is isolated from the two groups.
  4. Conductors of negligible resistance.
  5. Graph paper.

Warning: You are not allowed to open the black box.

EXPERIMENT

In the black box, there are two groups of passive elements (that are elements of the types: resistor RR, capacitor CC or inductor (induction coil) LL). The first group consists of three elements Z1,Z2,Z3Z_1, Z_2, Z_3 connected in a star circuit as shown in Figure 1. The elements are led out to the connectors A, B, C and D, with A - the common connector of the ABCD group. The second group consists of three elements Z1′Z'_1, Z2′Z'_2, Z3′Z'_3 connected in the same manner to connectors A', B', C' and D', with A'- the common connector of the A'B'C'D' group (see Figure 2).

Star circuit of the first group: a central node joined to connector B through element Z1 (left), to connector D through element Z3 (right), to connector C through element Z2 (up), and directly by a wire to connector A (down).
Figure 1

1. By using the oscilloscope and the function generator, determine the type and the parameter (that is resistance of RR, capacity of CC, inductivity of LL) of each of the elements Z1,Z2,Z3Z_1, Z_2, Z_3 and Z1′Z'_1, Z2′,Z3′Z'_2, Z'_3. [5.0 pts]

Star circuit of the second group: a central node joined to connector B' through element Z'1 (left), to connector D' through element Z'3 (right), to connector C' through element Z'2 (up), and directly by a wire to connector A' (down).
Figure 2

2. Connect five points B, C, B', C' and D' together. We obtain a new black box with terminals DD’A’ (called DD’A’).

a. Draw the electric circuit of this black box.

b. Apply a sine wave from the generator to connectors D and A'.

Plot a graph of the ratio of the voltage amplitudes K=UD′A′UDA′K = \dfrac{U_\mathrm{D'A'}}{U_\mathrm{DA'}} and the phase shift φ\varphi between these voltages as functions of the frequency ff of the signal.

c. The graphs possess a particular point at a certain frequency f0f_0. Determine the value of the frequency f0f_0, the ratio K=UD′A′UDA′K = \dfrac{U_\mathrm{D'A'}}{U_\mathrm{DA'}} and the phase shift φ\varphi at this frequency.

d. Derive the relation between f0f_0 and the parameters of the elements in the black box and calculate the values of f0f_0.. [5.0 pts]

Решение

Внимание: Непълно решение

В архива няма официално решение на тази задача.

Оригинал в Архива: exp2.pdf · официални решения: exp2_sol.pdf