C(x) Uo Ud R. Cfix Figure 3: Bridge circuit with variable capacitance c(a). Exercise 2.3 Bridge Circuit The circuit shown in Fig. 3 is given. All impedances are fixed except for C(r), which is a capacitance that changes due a fill level measurement (see Exercise Exercise 3.1). Calculate the diagonal voltage Ua in dependence of the variable capacitance C(a).

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Please answer exercise 2.3

C(x)
Uo
U.
Cfix
Figure 3: Bridge circuit with variable capacitance c(x).
Exercise 2.3 Bridge Circuit
The circuit shown in Fig. 3 is given. All impedances are fixed except for C(xr), which
is a capacitance that changes due a fill level measurement (see Exercise Exercise 3.1).
Calculate the diagonal voltage Ua in dependence of the variable capacitance C(x).
Transcribed Image Text:C(x) Uo U. Cfix Figure 3: Bridge circuit with variable capacitance c(x). Exercise 2.3 Bridge Circuit The circuit shown in Fig. 3 is given. All impedances are fixed except for C(xr), which is a capacitance that changes due a fill level measurement (see Exercise Exercise 3.1). Calculate the diagonal voltage Ua in dependence of the variable capacitance C(x).
Exercise 3.1 Fill Level Measuring
To measure the fill level of a tank, a capacitive measurement method should be applied.
The height of the tank is 2m, the diameter is 1m. The medium is electrically non-
conductive and its permittivity is e, = 3. With the help of metal plates, that are 1.8m
long and 0.5m wide the fill level should be measured. The distance between the plates
is 0.15m and the distance between the bottom of the tank and the plates is 0.03m. The
permittivity of air is eair = 1, the vacuum permittivity is eo = 8.85 - 10-12
Vm
a) Draw an expressive sketch.
b) Derive a function of the capacity C depending on the fill level r.
c) Sketch the curve of the capacity C depending on the fill level r.
Transcribed Image Text:Exercise 3.1 Fill Level Measuring To measure the fill level of a tank, a capacitive measurement method should be applied. The height of the tank is 2m, the diameter is 1m. The medium is electrically non- conductive and its permittivity is e, = 3. With the help of metal plates, that are 1.8m long and 0.5m wide the fill level should be measured. The distance between the plates is 0.15m and the distance between the bottom of the tank and the plates is 0.03m. The permittivity of air is eair = 1, the vacuum permittivity is eo = 8.85 - 10-12 Vm a) Draw an expressive sketch. b) Derive a function of the capacity C depending on the fill level r. c) Sketch the curve of the capacity C depending on the fill level r.
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