Основы измерений. Долгополов В.Т. - 24 стр.

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JZkkfhljbf ko_fm k ^\mfy wd\b\Ze_glgufb bklhqgbdZfb rmfZ V
1
b V
2
, ^\mfy dexqZfb S
b khijhlb\e_gbyfb R , kh_^bg_ggufb kh]eZkh\Zgguf ih hljZ`_gbx dZ[_e_f (Jbk.21 ..).
DZ`^h_ ba khijhlb\e_gbc ihklhyggh ]_g_jbjm_l b ihkueZ_l d ^jm]hfm khijhlb\e_gbx
\hegm gZijy`_gby kh kj_^g_d\Z^jZlbqguf agZq_gb_f 1/2V
RMS
, jZkijhkljZgyxsmxky ih
dZ[_ex kh kdhjhklvx v. AZfdg_f h[Z dexqZ S. Kbkl_fZ ij_\jZlbeZkv \ j_ahgZlhj k
j_ahgZgkgufb qZklhlZfb f
n
=n v /2l. Qbkeh qZklhl \ bgl_j\Ze_ 'f jZ\gh 'f / (v/2l). GZ
dZ`^mx j_ahgZgkgmx qZklhlm ijboh^blky ^\_ kl_i_gb k\h[h^u , Z gZ dZ`^mx kl_i_gv
k\h[h^u \ kj_^g_f wg_j]by 1/2kT. Dh]^Z dexqb jZahfdgmlu, lh aZ \j_fy 2l/v dZ`^uc ba
j_abklhjh\ \dZqb\Z_l \ dZ[_ev wg_j]bx, jZ\gmx gZdhie_gghc \ dZ[_e_, (2l/v)*V
2
RMS
/4R.
1/2kT*2*'f / (v/2l) = (2l/v)*V
2
RMS
/4R, beb V
RMS
= (4kTR
'
f)
1/2
.
Ihf_ob b f_lh^u [hjv[u k gbfb.
Djhf_ rmfh\ baf_j_gby hkeh`gyxl lZd gZau\Z_fu_ ihf_ob. < kmsghklb, lh qlh
fu gZau\Z_f ihf_oZfb y\ey_lky \ebygb_f \g_rgbo nZdlhjh\, \ ijhkl_cr_f kemqZ_ ,
\ebygb_f hdjm`Zxs_c kj_^u. GZijbf_j, qm\kl\bl_evghklv baf_jbl_evghc mklZgh\db
fh`_l aZ\bk_lv hl l_fi_jZlmju b \eZ`ghklb, Z h[Z wlb iZjZf_ljZ \h \j_fy baf_j_gbc
baf_gyxlky. Beb kb]gZe gZ \uoh^_ aZ\bkbl hl \b[jZpbc, beb `_ hl gZijy`_gby iblZgby.
<h \k_o wlbo kemqZyo fu b ]h\hjbf h ihf_oZo.
Ihf_oZ fh`_l [ulv Z^^blb\ghc b/beb fmevlbiebdZlb\ghc. < i_j\hf kemqZ_ kb]gZe
ihf_ob gZ \oh^_ ijhklh kdeZ^u\Z_lky k ihe_aguf kb]gZehf. Ijbf_jhf Z^^blb\ghc
ihf_ob fh`_l kem`blv l_jfh W>K. Ijb fmevlbiebdZlb\ghc ihf_o_ [_a ihe_agh]h
kb]gZeZ gZ \oh^_ g_l b \uoh^gh]h kb]gZeZ. LZd [u\Z_l, _keb ihf_oZ \eby_l gZ
qm\kl\bl_evghklv. QZklh \ebygb_ jZaebqguo nZdlhjh\ gZ baf_jbl_evgmx kbkl_fm aZ^Zxl
keh\_kgufb hij_^_e_gbyfb. GZijbf_j, ijb\h^yl qm\kl\bl_evghklv baf_jbl_evghc
kbkl_fu d gZijy`_gbx iblZgby beb l_fi_jZlmjguc dhwnnbpb_gl qm\kl\bl_evghklb
baf_jbl_evghc kbkl_fu C
T
=S
-1
dS/dT.
KZfuc gZ^_`guc f_lh^ [hjv[u k ihf_oZfb khklhbl \ baheypbb baf_jbl_evghc
ko_fu hl \g_rgbo \ha^_ckl\bc. Wlhc p_eb kem`bl l_jfhklZlbjh\Zgb_, bkihevah\Zgb_ ijb
baf_j_gbyo ki_pbZevguo wdjZgbjh\Zgguo ihf_s_gbc, bkihevah\Zgb_ klZ[bebaZlhjh\
gZijy`_gby k_lb beb bklhqgbdh\ [_ki_j_[hcgh]h iblZgby, bkihevah\Zgb_ «ieZ\Zxsbo»
nmg^Zf_glh\ ^ey mklZgh\db baf_jbl_evghc kbkl_fu, hl^_e_gguo hl bklhqgbdh\
\b[jZpbc, ijZ\bevgh_ aZa_fe_gb_ baf_jbl_evghc ko_fu, gZdhg_p.
< kemqZ_, _keb \hafh`ghklb baheypbb baf_jbl_evghc kbkl_fu bkq_jiZgu, lh
bkihevamxl jZaebqgu_ kbkl_fu Z\lhfZlbq_kdhc dhfi_gkZpbb ihf_o..
IZjZee_evgZy dhfi_gkZpby khklhbl \ jZks_ie_gbb baf_jbl_evghc kbkl_fu gZ ^\_
iZjZee_evgu_ qZklb, dZ`^Zy ba dhlhjuo ih^\_j]Z_lky ^_ckl\bx h^ghc b lhc `_ ihf_ob.
Dhfi_gkZpby ih hlghr_gbx d Z^^blb\ghc ihf_o_ [m^_l ^hklb]gmlZ, _keb S
d1
= dy
1
/dd = -
S
d2.
FmevlbiebdZlb\gZy ihf_oZ [m^_l kdhfi_gkbjh\ZgZ, _keb dS
1
/dd = - dS
2
/dd.
J_Zebam_lky b iZjZee_evgZy dhfi_gkZpby, gZijbf_j \ ^bnn_j_gpbZevguo ljZgabklhjguo
ij_^mkbebl_eyo, k h[sbf j_abklhjhf \ wfbl_jghc p_ib. <uimkdZxlky ^ey wlhc p_eb
^Z`_ ki_pbZevgu_ iZju ihe_\uo ljZgabklhjh\ \ h[s_f dhjimk_ (kf. ko_fm gZ Jbk. 22.).
Ihke_^h\Zl_evgZy dhfi_gkZpby khklhbl \ jZa[b_gbb baf_jbl_evghc kbkl_fu gZ ^\_
ihke_^h\Zl_evgh \dexq_ggu_ qZklb, ih^\_j`_ggu_ \ebygbx h^ghc b lhc `_ ihf_ob.
:^^blb\gZy ihf_oZ ih^Z\ey_lky , _keb S
1
-1
dS
1
/dd S
2
= C
1d
S
2
= -S
2d
. >ey ih^Z\e_gby
fmevlbiebdZlb\ghc ihf_ob g_h[oh^bfh C
1d
= - C
2d
. 
JZkkfhljbf ko_fm k ^\mfy wd\b\Ze_glgufb bklhqgbdZfb rmfZ V1 b V2 , ^\mfy dexqZfb S
b khijhlb\e_gbyfb R , kh_^bg_ggufb kh]eZkh\Zgguf ih hljZ`_gbx dZ[_e_f (Jbk.21 ..).
DZ`^h_ ba khijhlb\e_gbc ihklhyggh ]_g_jbjm_l b ihkueZ_l d ^jm]hfm khijhlb\e_gbx
\hegm gZijy`_gby kh kj_^g_d\Z^jZlbqguf agZq_gb_f 1/2VRMS, jZkijhkljZgyxsmxky ih
dZ[_ex kh kdhjhklvx v. AZfdg_f h[Z dexqZ S. Kbkl_fZ ij_\jZlbeZkv \ j_ahgZlhj k
j_ahgZgkgufb qZklhlZfb fn =n v /2l. Qbkeh qZklhl \ bgl_j\Ze_ 'f jZ\gh 'f / (v/2l). GZ
dZ`^mx j_ahgZgkgmx qZklhlm ijboh^blky ^\_ kl_i_gb k\h[h^u , Z gZ dZ`^mx kl_i_gv
k\h[h^u \ kj_^g_f wg_j]by 1/2kT. Dh]^Z dexqb jZahfdgmlu, lh aZ \j_fy 2l/v dZ`^uc ba
j_abklhjh\ \dZqb\Z_l \ dZ[_ev wg_j]bx, jZ\gmx gZdhie_gghc \ dZ[_e_, (2l/v)*V2RMS/4R.
1/2kT*2*'f / (v/2l) = (2l/v)*V2RMS/4R, beb VRMS = (4kTR'f)1/2.
       Ihf_ob b f_lh^u [hjv[u k gbfb.
       Djhf_ rmfh\ baf_j_gby hkeh`gyxl lZd gZau\Z_fu_ ihf_ob. < kmsghklb, lh qlh
fu gZau\Z_f ihf_oZfb y\ey_lky \ebygb_f \g_rgbo nZdlhjh\, \ ijhkl_cr_f kemqZ_ ,
\ebygb_f hdjm`Zxs_c kj_^u. GZijbf_j, qm\kl\bl_evghklv baf_jbl_evghc mklZgh\db
fh`_l aZ\bk_lv hl l_fi_jZlmju b \eZ`ghklb, Z h[Z wlb iZjZf_ljZ \h \j_fy baf_j_gbc
baf_gyxlky. Beb kb]gZe gZ \uoh^_ aZ\bkbl hl \b[jZpbc, beb `_ hl gZijy`_gby iblZgby.
K. Ijb fmevlbiebdZlb\ghc ihf_o_ [_a ihe_agh]h
kb]gZeZ gZ \oh^_ g_l b \uoh^gh]h kb]gZeZ. LZd [u\Z_l, _keb ihf_oZ \eby_l gZ
qm\kl\bl_evghklv. QZklh \ebygb_ jZaebqguo nZdlhjh\ gZ baf_jbl_evgmx kbkl_fm aZ^Zxl
keh\_kgufb hij_^_e_gbyfb. GZijbf_j, ijb\h^yl qm\kl\bl_evghklv baf_jbl_evghc
kbkl_fu d gZijy`_gbx iblZgby beb l_fi_jZlmjguc dhwnnbpb_gl qm\kl\bl_evghklb
baf_jbl_evghc kbkl_fu CT =S-1dS/dT.
       KZfuc gZ^_`guc f_lh^ [hjv[u k ihf_oZfb khklhbl \ baheypbb baf_jbl_evghc
ko_fu hl \g_rgbo \ha^_ckl\bc. Wlhc p_eb kem`bl l_jfhklZlbjh\Zgb_, bkihevah\Zgb_ ijb
baf_j_gbyo ki_pbZevguo wdjZgbjh\Zgguo ihf_s_gbc, bkihevah\Zgb_ klZ[bebaZlhjh\
gZijy`_gby k_lb beb bklhqgbdh\ [_ki_j_[hcgh]h iblZgby, bkihevah\Zgb_ «ieZ\Zxsbo»
nmg^Zf_glh\ ^ey mklZgh\db baf_jbl_evghc kbkl_fu, hl^_e_gguo hl bklhqgbdh\
\b[jZpbc, ijZ\bevgh_ aZa_fe_gb_ baf_jbl_evghc ko_fu, gZdhg_p.
       < kemqZ_, _keb \hafh`ghklb baheypbb baf_jbl_evghc kbkl_fu bkq_jiZgu, lh
bkihevamxl jZaebqgu_ kbkl_fu Z\lhfZlbq_kdhc dhfi_gkZpbb ihf_o..
       IZjZee_evgZy dhfi_gkZpby khklhbl \ jZks_ie_gbb baf_jbl_evghc kbkl_fu gZ ^\_
iZjZee_evgu_ qZklb, dZ`^Zy ba dhlhjuo ih^\_j]Z_lky ^_ckl\bx h^ghc b lhc `_ ihf_ob.
Dhfi_gkZpby ih hlghr_gbx d Z^^blb\ghc ihf_o_ [m^_l ^hklb]gmlZ, _keb Sd1= dy1/dd = -
Sd2. FmevlbiebdZlb\gZy ihf_oZ [m^_l kdhfi_gkbjh\ZgZ, _keb dS1/dd = - dS2/dd.
J_Zebam_lky b iZjZee_evgZy dhfi_gkZpby, gZijbf_j \ ^bnn_j_gpbZevguo ljZgabklhjguo
ij_^mkbebl_eyo, k h[sbf j_abklhjhf \ wfbl_jghc p_ib. ey ih^Z\e_gby
fmevlbiebdZlb\ghc ihf_ob g_h[oh^bfh C1d = - C2d.

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