To determine dielectric constant of solid substance by resonance method
Answers
Resonance methods, useful for frequencies greater than 1 MHz, involve the injection of voltage or current by one of several methods into an LC (inductance-capacitance) resonant circuit. Measurements over a range of frequencies may be made by using coils with different inductance values, but ultimately the inductance required becomes impracticably small, and in the range 108-109 Hz re entrant cavities are often used. These are hybrid devices in which the plates holding the specimen still form a lumped capacitor, but the inductance and capacitances are distributed along a coaxial line. At higher frequencies, the wavelength is comparable to the dimensions of the apparatus, and transmission methods in coaxial lines and waveguides must be used.
In the frequency range from tenths of a hertz up to 107 Hz it is important to measure, in addition to C, the dielectric loss, which can be expressed by the tangent of the dielectric loss angle, tan δ. The quantities C and tan δ are measured by means of bridge circuits, particularly the Schering bridge.
In the high-frequency range (from 105 to 108 Hz) resonance methods are generally used to measure the capacitance C and the dielectric constant E. An oscillatory circuit that includes a standard capacitor is tuned to resonance and the corresponding value of capacitance C’ is determined. Then a capacitor with the dielectric C is connected in parallel with the standard capacitor and the circuit is again tuned to resonance. In the second case the capacitance C" of the standard capacitor will be smaller. The capacitance of the capacitor that is filled with the dielectric C is found from the formula
C=C’ - C"
The various resonance methods are differentiated according to the means of determining tan δ. In the substitution method the dielectric is replaced by an equivalent circuit consisting of a capacitance and a resistance. The resistance R is chosen such that when connected in series or parallel with a standard capacitor C1, whose capacitance is taken as equal to the capacitance of the dielectric C, the same resonance current is produced in the circuit as with the specimen dielectric. The circuit detuning method is based on the fact that the width of the circuit’s resonance curve is a function of its quality factor Q, which is related to the tangent of the dielectric loss angle by the equation
tan δ = l/Q
AIM: To determine the dielectric constant of different materials by resonance method
APPARATUS REQUIRED: RF Oscillator, Test Capacitor, Variable Capacitor, Test Dielectric
Material and Patch Cords
FORMULA: The dielectric constant is given by:
K =
.
0
Where, d = distance between two plates
A = Area of plate
C = Capacitance
ε0 = free space permittivity 8.854 X 10-12 Fm-1
Instructions:
1. Test capacitor's plate must be tight when filled with dielectric material.
2. Observations must be taken carefully.
3. Patch cords should be tightly connected.
Observations:
Dielectric
Sample
Gap
between
plates (d) in
(m)
C1
(without
sample)
(pF)
C2 or C3
(with
sample)
(pF)
C1 - C2 or
C3 - C2
(pF)
Teflon
(known)
K1 = 2.35
d1 = 3.1×10-3 248 C2 = 223 C1 - C2 = 25
0 =
(c1 − c2)d1
K1
=32.9x10-3
Bakelite
(unknown)
K2 = ?
d2 = 6.5×10-3 248
C2 = 215 C1 – C2 = 33
2 =
(c1 − c2)d2
ϵ0A
=6.51
C3 = 234 C3 - C2 = 19
2 = 1 +
(c3 − c2)d2
ϵ0A
=4.75
Result: The dielectric constant of material = 4.75
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