PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR

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August James
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PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR. THE PARALLEL-PLATE CAPACITOR.

the istance between them, ). Both plates have the same charge, Q, but with opposite sign, uniformly split on each plate, σ = ifference of potential (..p.) V σ = Q S Q σ.

Placing a ielectric between plates, capacitance is multiplie by a characteristic factor of the ielectric Sketch of a parallel plate capacitor material, calle relative

Usually, capacitors are built by rolling up two conuctor sheets with a ielectric between them, in orer to save space: S σ E = ε V V 2 2 a) Builing a capacitor b)

than the no electrolytic capacitors; their terminals have a well-efine polarity (there are pointe out positive an negative terminals).

Besies the parallel plate capacitors, there also are other ifferent geometries, as the spherical or cylinrical capacitors.

1 PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR. THE PARALLEL-PLATE CAPACITOR. The Parallel plate capacitor is a evice mae up by two conuctor parallel plates with total influence between them (the surface of each plate, S, is very high compare with the istance between them, ). Both plates have the same charge, Q, but with opposite sign, uniformly split on each plate, σ = ifference of potential (..p.) V σ = Q S Q σ. Electric fiel is uniform in the space between plates, E =, being their S ε σ Q V2 = E = =. The capacitance of a capacitor is the ε ε S quotient between charge an..p. between plates Q ε S C = = V V only epening on shape an size of capacitor. Placing a ielectric between plates, capacitance is multiplie by a characteristic factor of the ielectric Sketch of a parallel plate capacitor material, calle relative ielectric permittivity ε r ε (ε = ε ε r is the ielectric permittivity), being C = εs. As ε r >, capacitance will always increase. Usually, capacitors are built by rolling up two conuctor sheets with a ielectric between them, in orer to save space: S σ E = ε V V 2 2 a) Builing a capacitor b) Different capacitors c) Electrolytic capacitor A special kin of capacitors are the electrolytic capacitors, whose base is a chemical reaction, having higher capacitances than the no electrolytic capacitors; their terminals have a well-efine polarity (there are pointe out positive an negative terminals). The nonelectrolytic capacitors on t have neither positive nor negative terminal, an they can be connecte with any polarity. Besies the parallel plate capacitors, there also are other ifferent geometries, as the spherical or cylinrical capacitors. The coaxial cable of an antenna, or the coaxial cable you ll use on laboratory are cylinrical capacitors. There are ifferent systems to give the nominal value of capacitance for a capacitor (for example, through the color coe, in the same way than resistors), but the most usual is mae up by three reaings on the cover of capacitor, giving the capacitance, its relative error, an

2 the maximum voltage supporte by the capacitor. The relative error is given through a coe relating letters an relative errors: Letter Relative error J 5 % K % M 2 % For example, the capacitance of capacitor on picture is 6,8 µf, the coe K means % of relative error (*6,8/=,68,7 µf) an it can support up to V. So, capacitance of this capacitor, correctly rouning error an measurement, is: C= 6,8 ±,7 µf 2. CHARGING AND DISCHARGING A CAPACITOR a. CHARGING PROCESS The easiest way to charge a capacitor with capacitance C is applying a ifference of potential V between its terminals with a D.C. source. Then, each plate of capacitor will take a charge Q = CV. Theoretically, charging of capacitor will be instantaneous: q But on a circuit with resistors (R), this charging process isn t instantaneous, an a time is neee to fully charge the capacitor, becoming a transient phenomenon. On this picture, voltage on terminals of capacitor is graphe instea its charge, because it s easier measuring the voltage than charge, an both are irectly relate (V c =QC). The equation of this curve can be got from equation of circuit (to o it, you nee stuy theory of circuits, on next units). b. DISCHARGING PROCESS When a capacitor is charge, if we remove the D.C. source an capacitor is connecte to a resistor, an electric current is prouce; the store energy on capacitor is lost on resistor ue to Joule heating, until the current stops.

3 At any time uring ischarging process, the intensity flowing along the circuit i(t) equals the charge passing from a plate to another plate (negative because it s ecreasing); besies, the voltage on terminals of capacitor V c (t) must be equal to the voltage on terminals of resistor i(t)r. If is the charge of capacitor on time t: i(t) (t) V C t = i(t)r C R t V C (t) = C t By integrating this equation from time t= (when charge on capacitor is CV from a time t when the charge on capacitor is : CV t t = V Ce t V (t) = V c t e Prouct is known as time constant of circuit τ= (you can check that is imensionally a time, so being measure in secons). As V c(t = τ ) = V(e ) =,37V the time constant can be experimentally measure as the time when the voltage (or charge) on capacitor is only a 37% of initial voltage (or initial charge). Discharging process is theoretically an infinite process, but it s usually assume that capacitor is fully ischarge after five times the time constant, because after this time the remaining voltage (or charge) is almost zero: V c(t = 5τ ) = V(e ) =,7V 5

4 PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR. CARRYING OUT. OBJECTIVES The objective of this practice is the unerstaning of charging an ischarging processes of a capacitor an the meaning of time constant. It is also an objective to unerstan how the charge is conserve when two capacitors are connecte. 2. MATERIAL Gol source D.C. power supply Switch Digital Tektronix oscilloscope 6,8 an 2,2 μf capacitors 3. CARRYING OUT Take the 6,8 µf an 2,2 µf capacitors. Accoring the ata on cover of both capacitors, compute their absolute errors. a) Charge the 6,8 µf capacitor by connecting it to the Fixe 5V output of D.C. power supply. If we accept that the applie voltage (5 V) hasn t any error, compute the charge taken by the capacitor Q with its error (you must apply the propagation error theory). Disconnect the capacitor from power supply an be careful that terminals of capacitor are not shortcircuite, because then the capacitor woul be ischarge. Take the 2,2 µf capacitor an verify that it is fully ischarge, by only short-circuiting its terminals an connect both capacitors in parallel by using the connection box. Now, the charge on first capacitor is ivie between them, an we are going to measure the charge of each verifying that their aition equals the charge taken by the first capacitor. b) To o it, we ll ischarge each capacitor through the own resistance of oscilloscope (R osc ), usually calle input impeance. Besies, on screen of oscilloscope we ll see the ischarging curve, being possible the measurement of time constant of circuit. But we must verify that the switch is open before connect it in the circuit. When this circuit was assemble: Switch on the oscilloscope an verify its ajustments, as was explaine on before practice. Verify that on Menu CH/Acoplamiento option CC is selecte. Ajust the vertical scale to 2 V/iv. Ajust the horizontal scale to 5 s/iv. You will see now a point moving along the screen of oscilloscope from left to right. When this point was place on left sie of screen, close the switch of circuit an you ll see the ischarging curve on screen of oscilloscope. Wait until ischarging process finishes an then press the button Activar/Parar in orer to freeze the curve. Take a picture of this curve with your mobile phone. With the cursors of oscilloscope, measure the voltage V 6,8 when ischarging process starts (t=) an compute the charge taken by capacitor Q 6,8 (Q=CV). With the cursors measure the time constant τ 6,8 (remember that time constant is the time when

5 37% of initial voltage is reache along the ischarging process), an from this atum, the resistance of oscilloscope (R osc ). All these ata must be compute with their corresponing errors. c) Repeat the point b) with the 2,2 µf capacitor, measuring an computing V 2,2 Q 2,2 τ 2,2 an R osc their corresponing errors. To o it, after freezing an measure the ischarging curve, you shoul press the button Activar/Parar. Compare an relate magnitues measure on both capacitors. Do V 6,8 an V 2,2 are equal? Why? Do Q 6,8 an Q 2,2 are relate to Q? Why? Do both compute R osc match? ) If you have time enough, repeat the experiment but instea connecting both capacitors in parallel after one of them has been charge, connecting both ischarge capacitors in series an applying 5 V to this set of capacitors. Repeat an relate the measurements of voltage an charge on both capacitors. 4. REPORT A report of this practice must be one accoring the rules given on previous practices. On this report must appear the taken photos, the results of measurements, the explanation of computations one an the comparison between results.

UNIT 4:Capacitors and Dielectric

UNIT 4:Capacitors and Dielectric UNIT 4:apacitors an Dielectric SF7 4. apacitor A capacitor is a evice that is capable of storing electric charges or electric potential energy. It is consist of two conucting plates separate by a small