Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard measuring instruments. By using the fixed resistrs and capacitrs in varius series and parallel cnfiguratins, yu will establish by direct measurement simple relatins between the vltage and current in a circuit. Yu will then cmpare yur results with thse expected n the basis f circuit relatinships. Nte: Refer t the reference fr equatins relating current and vltage fr resistrs and capacitrs cnnected in series and in parallel. Cautin: Always turn ff vltage and discharge any capacitrs befre tuching circuit cnnectins. An insulated cnductr is supplied t discharge the capacitrs be sure t tuch nly the insulated grips. Resistance Cmbinatins In the circuits drawn in Figs. 1 and 2 belw, - V is a vltmeter that measures the ptential difference acrss its terminals. - A is an ammeter that measures the current passing thrugh it. A, A and A are three ammeters, each in a different branch f the circuit. - 1 2 3 R and R are 200 hm resistrs and R 2 is a 100 hm resistr. - 1 3 - The surce f vltage in these circuits (represented by the battery symbl) is the HP E3611A, adjusted t deliver apprximately three vlts DC, as measured by the vltmeter. - V is als used t represent vltage r ptential, while I represents current. (A) Lcate and trace ut the cnnectins f the circuit in Figure 1. Measure and tabulate current and vltage. D this fr 5 values f vltage yu will set with the HP 3611A pwer supply (eg 3,4,5, 6, and 7 Vlts). 131029 1
Brwn University Physics 0040 Figure 1 Figure 2 (B) D the same with the circuit f Figure 2. Measure and tabulate vltage and current readings with the ammeters in the psitins shwn. Be sure yu identify the ammeters crrectly. Resistance-Capacitance Circuits (A) Here we charge capacitrs and then explre what happens after the surce f the charge is remved, and the charged capacitrs are left cnnected t a resistr s that the 131029 2
Brwn University Physics 0040 stred charge can flw frm the capacitr plates. The charge thus will vary (decrease) with time after the charge surce is remved. The discharge f a capacitr C thrugh a resistr R is analyzed in Chapter 27. We may be a little ahead f the lectures here, but the ideas are simple enugh t fllw: The charge q remaining in the capacitr, at time t after discharge begins, decreases expnentially with a time cnstant equal t RC. Since the time-dependent current is I dq / dt (by definitin), it is easy t shw that the current, like the charge, decays expnentially. Instead f a cnstant current such as ne finds, fr instance, in the circuit f Fig. 1, I is nw a functin f time t: I t I c t / RC ( ) ; lg e ( I / I ) t / RC, (1) where t 0 crrespnds t the time at which the charge surce is discnnected while the RC circuit remains cnnected. The capacitr nw acts (temprarily!) as the pwer surce in the remaining circuit. (A) Fr the circuit in Fig. 3 (R=51 khms, 330 micrfarad each), use the Hewlett - Packard vltage supply fr V, with V equal t apprximately 30 vlts. After a few minutes, discnnect the supply using switch S and read the value f current immediately; this value is I. With a timer measure the time at which the current has drpped t I / 2, I / 4, I /8 and I /16. (B) Repeat fr the circuit f Fig. 4. (R=51 khms, C 1 330micrfarad, C 2 330 micrfarad, and V ~ 30 vlts.) Figure 3 ` Figure 4 131029 3
Brwn University Physics 0040 ANALYSIS OF DATA Remember: Whenever yu make cmparisns between measured and calculated values, yu must specify the estimated uncertainties in yur experimental measurements, and take accunt f these in analyzing the cmparisns. Resistance Cmbinatins (A) Frm the current and vltage measurements fr the circuit f Fig. 1, determine the effective resistance f the three-resistance cmbinatin and cmpare this with the value f the ttal resistance calculated frm the given values f the resistrs. Plt the vltage vs current measurements n graph paper in yur lab ntebk during the lab perid, the slpe f this line is the effective resistance. (B) (1) Frm V and I 1 in the circuit f Fig. 2, determine the effective resistance f the three-resistr cmbinatin and cmpare this with the calculated value f the ttal resistance. Again plt I 1 vs V fr 5 vltage values yu set with the HP3611A pwer supply n graph paper in yur lab ntebk. The slpe will be the effective resistance. (2) Cmpare I 1, I 2, and I3 with the expected relatins amng them, and the measured value f V. 131029 4
Brwn University Physics 0040 (3) Frm the current measurements, cmpute the ptential drps acrss R 1, R2, and R 3 and cmpare with the expected relatins amng them, and with the measured value f V. Resistance-Capacitance Circuits The expected relatin (Eq. (1) can be tested by calculating lge ( I / I ) fr each reading and pltting against t, but semilgarithmic graph paper may be used instead. (The instructr will explain its use if yu are nt familiar with it.) The result shuld be a straight line, reflecting the expnential frm f Eq. (1). Fr bth the (A) and (B) parts f the RC circuit data: (1) Plt yur data and frm the slpe f the line determine the value f RC (hms x farads = secnds). (Frm Eq. (1), the slpe = 1/ RC.) This must be dne during the lab perid and shuld be checked by yur TA. (2) Using the knwn value f R, calculate the effective capacitance f the tw-capacitr cmbinatin, in each case. (3) Cmpare the effective capacitance, in each case, with the calculated values based n the knwn individual capacitances. Reference: Yung and Freedman, University Physics Extended Versin with Mdern Physics, Chapters 25-27 131029 5