Determinacion De Capactancia

Electricity
Electrostatics Plate capacitor

LEYBOLD Physics Leaflets

P3.1.7.1

Determining the capacitance of a plate capacitor

Measuring the charge with the electrometer amplifier

Objects of the experiments
Measuring the charge Q on a plate capacitor as a function of the applied voltage U. Determining the capacitance C as a function of the area A of the plates. Determining thecapacitance C with different dielectrics between the plates. Determining the capacitance C as function of the distance d between the plates.

Principles
The simplest design of a capacitor is that of a plate capacitor. Its capacitance C= Q U Q: charge on the capacitor, U: applied voltage (I)

depends on the area A of the plates, the distance d between the plates and the – non-conductive –material between the plates. The capacitance of a plate capacitor is C = εr ⋅ ε0 ⋅ A d As : permittivity of free space, Vm (II),

ε0 = 8.85 ⋅ 10 − 12

as long as the distance between the plates is much smaller than the dimensions of the plates and the field E between the plates can be considered to be homogeneous. The permittivity εr describes the change of the capacitance relatively to the vacuumvalue caused by the introduction of the material. The relation (II) is studied in the experiment by means of a demountable capacitor with variable geometry. Capacitor plates with areas A = 400 cm2 and A = 800 cm2 are available. The distance d between the plates can be increased with spacers in steps of 1 mm. First the charge Q on the capacitor is measured as a function of the voltage U. Thecapacitance C is then determined as the slope of the straight line through the origin and through the data points. In order to confirm the proportionality C A (III),

1209-Wei

which is derived from Eq. (II), the measurement is carried out at a fixed distance d with different areas A of the plates. In addition, the permittivities εr of different dielectrics are determined by placing the dielectricsbetween the capacitor plates. Variation of the distance d between the plates at a constant area A allows to confirm the proportionality C 1 d (IV).

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P3.1.7.1

LEYBOLD Physics Leaflets
Charges are measured with an electrometer amplifier operated as a coulombmeter. Any voltmeter may be used to display the output voltage UA. From the reference capacitance CA 544 23 522 27 532 14 57825 578 10532 16 531 100 531 100 504 48 Q = CA ⋅ UA (V).

Apparatus
1 demountable capacitor . . . . . . . . . . 1 power supply 450 V DC . . . . . . . . . . 1 electrometer amplifier . . . 1 STE capacitor 1 nF, 630 V 1 STE capacitor 10 nF, 630 V 1 connection rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

is obtained. For example, at CA = 10 nF, UA = 1 V corresponds tothe charge Q = 10 nAs. If other capacitances are used, other measuring ranges are accessible.

1 voltmeter, DC, range U = ± 8 V, e. g. . . . 1 voltmeter, DC, range U 300 V, e. g. . . 1 two-way switch . . . . . . . . . . . . . . connection leads

Setup
The experimental setup is illustrated in Fig. 1.

– Mount the pair of small plates (A = 400 cm2), and set the
distance d between the platesto 4 mm with the spacers.

– Connect the negative pole of the power supply 450 V to the
right plate and to the earth of the electrometer amplifier. Connect the connection rod to the earth as well. Connect the positive pole of the power supply 450 V to socket B of the two-way switch. Connect socket A of the two-way switch to the left plate and socket C to the input of the electrometer amplifier.Plug the reference capacitor CA = 10 nF in at the electrometer amplifier, and connect the voltmeter to the output. Connect the other voltmeter to the power supply 450 V for measuring the voltage U.

– – – –
Fig. 1 Experimental setup for the determination of the capacitance of a plate capacitor

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Carrying out the experiment
a) Measuring the charge as a...