Ohmmeter

Resistance Measurement ENE 240 Electrical and Electronic Measurement (2/2008) Class 8, January 14, 2009 Werapon Chiracharit, Ph. D. , ENE, KMUTT werapon. [email  protected] ac. th 1 Analogue Ohmmeter †¢ Permanent-magnet moving-coil (Galvanometer, ? ? I ) with a total resistance Rg †¢ Series type ohmmeter with battery E †¢ Resistance R to be measured †¢ Rz to be zero-ohm-adjusted Rz R E + – Rg 2 1 Zero-Ohm Adjustment †¢ Short circuit at the terminals 0? Resistance reading is zero, R = 0 †¢ Adjust Rz for a full-scale current reading E = Ifsd (Rz + Rg) Ifsd = E / (Rz + Rg) †¢ E and Rg are constant †¢ Change Rz (change Ifsd) for multirange 3 Zero-Ohm Adjustment (Cont’d) †¢ for the series type ohmmeter E = I (R + Rz + Rg) I = E / (R + Rz + Rg) †¢ R increased, I decreased, ? decreased †¢ Relationship between I and R is non-linear, it means a non-linear resistance scale. †¢ Rz and Rg are small, then for high resista nces, the scale points are very close together! 4 2 Shunt Type Ohmmeter †¢ When R = ? (open circuit), R1 is adjusted for a full-scale reading. E = Ifsd (R1 + Rg) Ifsd = E / (R1 + Rg) R1 R Ig IR Rg E 5 I Shunt Type Ohmmeter (Cont’d) †¢ When R is connected, the current passing through the meter is reduced by shunt resistor. 1/Rparallel = 1/R + 1/Rg Rparallel = RRg / (R + Rg) and E = I (R1 + Rparallel) = I (R1 + RRg/(R + Rg)) = I (R1R + R1Rg + RRg) / (R + Rg) = I (R1Rg + R(R1 + Rg)) / (R + Rg) 6 3 Shunt Type Ohmmeter (Cont’d) †¢ The current I is divided into 2 parts. IgRg = IRR Ig = I – IR = I – IgRg/R therefore Ig = E(R + Rg)/(R1Rg + R(R1 + Rg)) – IgRg/R Ig(1+Rg/R) = E(R + Rg)/(R1Rg + R(R1 + Rg)) Ig(R+Rg)/R = E(R + Rg)/(R1Rg + R(R1 + Rg)) Ig = ER / (R1Rg + R(R1 + Rg)) †¢ Meter reading depends on the value of R, though R is a low resistance. 7 Series Ohmmeter Shunt Ohmmeter 8 4 Bridge Method †¢ Bridge methods are used for measurement of resistance, capacitance, inductance, etc. †¢ e. g. the network will be balanced when the detector reading becomes zero. Component Being Measured Bridge Network Detector 9 Wheatstone Bridge †¢ DC supply, Vs †¢ Output voltage, Vo B R1 I1 A I2 R3 D + Vs – R4 10 R2 Vo C 5 Wheatstone Bridge (Cont’d) †¢ When Vo = 0, the potential at B must equal to the potential at D I1R1 = I2R3 I1R2 = I2R4 Hence I1R1 = I2R3 = (I1R2/R4) R3 R1/R2 = R3/R4 †¢ The balance condition is independent of Vs 11 Wheatstone Bridge (Cont’d) †¢ R2 and R4 are known-fixed resistances. †¢ R3 can be adjusted to give the zero potential difference condition. †¢ R1 is the input resistance to be measured. A R1 Adjust R3 B Vo = 0 G B D Wheatstone Bridge 12 6 Wheatstone Bridge (Cont’d) †¢ †¢ †¢ †¢ †¢ Change in R1, change R3 Precision about 1 ? to 1 M? Accuracy is up to the known resistors. Sensitivity of the null detector Error comes from changes in resistances by changes in temperatures. 13 Wheatstone Bridge (Cont’d) †¢ If no galvanometer at the output, VAB = Vs R1/(R1+R2) VAD = Vs R3/(R3+R4) Thus, Vo = VAB – VAD Vo = Vs ( R1/(R1+R2) – R3/(R3+R4) ) †¢ The relationship between Vo and R1 is non-linear 14 7 Wheatstone Bridge (Cont’d) †¢ A change R1 to R1+? R1 gives a change Vo to Vo+? Vo Vo+? Vo=Vs((R1+? R1)/((R1+? R1)+R2) – R3/(R3+R4)) Then (Vo+? Vo)–Vo = Vs R1+? R1 – R3 R1+? R1+R2 R3+R4 –Vs R1 – R3 R1+R2 R3+R4 = Vs R1+? R1 – R1 R1+? R1+R2 R1+R2 15 Wheatstone Bridge (Cont’d) †¢ If small changes ? R1 >R3 and Rs1//R3 to Rs1 avoid the leakage effect †¢ Rs2 may affect the R3 R4 detector sensitivity 24 12 Bridge Compensation †¢ The resistance of long leads will be affected by changes in temperatures †¢ To avoid this, 3 leads are required to connect to the coils †¢ They are all the same length and resistance 25 Bridge Compensation (Cont’d) †¢ Any changes in lead resistance will affect all 3 leads equally and occur in 2 arms of bridge and will cancel out. 3 R1 1 2 R3 Vs Vo R4 26 R2 13