ภาพนิ่ง 1 - ecpe.nu.ac.th

ภาพนิ่ง 1 - ecpe.nu.ac.th

Indicating Instrumen DArsonval - Ammeter - Voltmeter - Ohmmeter - Multimeter , , Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Multimeter

DC Ammeter DC Ammeter (DC Ammeter) DArsonval (PMMC) A (range) DArsonval ( ) Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU (PMMC) A

R m I m Im Rm +Vm - (Ifs = ( DC Ammeter R m

I m DC Ammeter RShunt, Rsh > R sh Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Vm I m Rm

Ish Rsh Rsh + + Vm Vsh - - Vsh Vm I I m I sh

Vsh Rsh I sh Rsh I m Rm I sh I I m I m Rm I sh Im Rm I Im

n Im n .I RI sh m Im Rsh Rm I Im Im Rsh Rm n.I m I m

Im Rm I m n 1 1 Rm n 1 1 Rsh 1 mA 100 I 0 I 100 mA sh Rsh Im = 1 mA

Rm = 100 Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU I Ish Im = 1 mA Rsh I sh I I m Rm = 100 100 1 99 mA

V Rsh sh I sh I m Rm I sh 1 mA 100 99 mA 1.01 2 99 ohm

0.1 mA 1 ohm I 0.5 0.1 mA 0.05 mA m Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Vm I m Rm 0.05 mA 99 Vm I sh

Rsh 4.95 mV 4.95mV 1 4.95 mA I I sh I m 4.95 mA + 0.05 mA 5 mA (Swamping Resistance) (Cu) (Mn) - (I2R)

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Single Shun (Selector Sw (Make before Break Switch) Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Ayrton Shu Universal Shunt Im

Rm Rsh Rc Rb I2 I3 I1 + Ra I1 I1 -

Ra, Rb, Rc (I1, I1 Rsh1 Im Rm Rsh1 Rc Rb I2 I3 I1 +

Ra I1 Rsh1 = Ra + Rb + Rc ( I1 - I m ) Rsh1 = I m Rm I m Rm Rsh1 = ( I1 - I m ) I1 I m Rm Rsh1 = Ra + Rb + Rc = ( I1 - I m ) I2 Rsh2 Im

Rm Im Rm Rsh2 Rc Rsh2 Rb I2 I2 I3 I2 + Ra Ra

I1 - Rc I2 I2 + Rsh 2 = Rc + Rb Rb - I2 Im

Rm Ra ( I 2 - I m ) Rsh 2 = I m ( Ra + Rm ) Rsh2 Rc Rb VRb +Rc = VRm +Ra I2 I2 I 2 Rsh 2 - I m Rsh 2 = I m Ra + I m Rm

I2 Ra = Rsh1 - Rb - Rc = Rsh1 - ( Rb + Rc ) + - = Rsh1 - Rsh 2 I 2 Rsh 2 - I m Rsh 2 = I m ( Rsh1 - Rsh 2 ) + I m Rm = I m Rsh1 - I m Rsh 2 + I m Rm Rsh2 sh2

I 2 Rsh 2 = I m Rsh1 + I m Rm I m ( Rsh1 + Rm ) Rsh 2 = I2 Ra Ra = Rsh1 - Rsh 2 I3 Rsh3 Im Rm Im Rsh3 Rc Rb Ra

Rsh3 I3 Rb I2 I3 I3 Rm + I1 - Ra

Rc I3 I3 + Rsh 3 = Rc I3 - Im Rm Rb Ra

( I 3 - I m ) Rsh 3 = I m ( Rm + Ra + Rb ) Rsh3 Rc VRc = VRm +Ra +Rb I 3 Rsh 3 - I m Rsh 3 = I m Rm + I m Ra + I m Rb I3 I3 I3 + - Ra + Rb + Rc = Rsh1 Ra + Rb = Rsh1 - Rc = Rsh1 - Rsh 3

I 3 Rsh 3 - I m Rsh 3 = I m ( Rsh1 - Rsh 3 ) + I m Rm = I m Rsh1 - I m Rsh 3 + I m Rm Rsh3 2 I 3 Rsh 3 = I m Rsh1 + I m Rm I m ( Rsh1 + Rm ) Rsh 3 = I3 = Rc ** , Rsh3 (Rc) Rb Rb = Rsh 2 - Rsh 3 Rb = Rsh 2 - Rc

Ayrton Shun I1 () I m Rm Rsh1 = Ra + Rb + Rc = I1 - I m 1 = Rm n - 1 I2 I m ( Rm + Rsh1 ) Rsh 2 = Rb + Rc = I2 Ra = Rsh1 - Rsh 2

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Ayrton Shun I3 () I m ( Rm + Rsh1 ) Rsh 3 = Rc = I3 Rb = Rsh 2 - Rsh 3 I4, I5 Rsh4, Rsh5 I2, I3 Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU 3 Ra, Rb, Rc Ayrt Im=100 mA Rm=1 kW

+ Rsh Rc + I3 1A Rb I2 100mA Ra I1 10mA Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Im=100 mA

Rm=1 kW + Rsh Rc + I3 1A Rb I2 100mA Ra I1 10mA I1 (10 mA) Im

Rsh1 = Ra + Rb + Rc = Rm I1 - I m 100 mA = 1 kW 10 mA - 100 mA = 10.1 W I2 (100 mA) Ra Rsh2

I m ( Rm + Rsh1 ) Rsh 2 = Rb + Rc = I2 100mA ( 1 kW+ 10.1 W) = 100 mA = 1.01 W Ra = Rsh1 - Rsh 2 = 10.1W- 1.01W = 9.09 W I3 (1 A) Rc (Rsh3 ) Rb I m ( Rm + Rsh1 ) Rsh 3 = Rc = I3 100mA ( 1 kW+ 10.1 W) = 1A = 0.101 W

Rb = Rsh 2 - Rsh 3 = 1.01W- 0.101W = 0.101 W Ayrton Shunt Im=100 mA Rm=1 kW + Rsh 0.101 W + 0.909 W I3 1A 9.09 W

I2 100mA I1 10mA nsertion Effects, Ammeter Loading E / Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU R1 X

Ie E E Ie = R1 Y R1 E X Im Rm

Y E Im = R1 + Rm 4 Rc 78 Ohm Ra=1 kW E=3V Rb=1 kW Rc=1 kW

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU E I= Ra +( Rb // Rc ) Ra=1 kW E 3V I Rb=1 kW Rc=1 kW E = Rb Rc

Ra + Rb + Rc 3V = 1 kW 1 kW 1 kW+ 1 kW + 1 kW 3V = 1 kW+ 0.5 kW = 2 mA Ra=1 kW E

3V 2mA Rb=1 kW Rc=1 kW Rb I Rc = I Rb + Rc 1 kW = 2 mA

1 kW+1 kW = ( 0.5) 2 mA (Current Divider) Rc = 1 mA E I= Ra +( Rb // ( Rc + Rm ) ) Ra=1 kW I

E 3V Rb=1 kW Rc=1 kW Rm= 78 W E = Rb ( Rc + Rm ) Ra + Rb + Rc + Rm 3V =

1 kW 1.078 kW 1 kW+ 1 kW + 1.078 kW 3V = 1 kW+ 0.519 kW = 1.975 mA Ra=1 kW I =1.975mA E 3V Rb=1 kW Rc=1 kW Rm= 78 W

Rb I Rc = I Rb +( Rc + Rm ) (Current Devider) Rc

1 kW = 1.975 mA 1 kW+1.078 kW = 0.95 mA (Percentage of Error Xt - Xm % Error = 100 Xt = 1 mA - 0.95 mA 100 1 mA

= 0.05 mA 100 1 mA = 5% Rsh (Rin) Rin Rin = Rm // Rsh Rm Rsh Rin = Rm + Rsh (Friction Error)

(Temperature Error) Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU ()

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU DC Voltmeter (DC Voltmeter) DArsonval (PMMC) ImRm Rs DArsonval meter (limit) Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU DC Voltmeter (Sensitivity ; S)

1 1 S= S = ( W/ V ) I I fs m ( W/ V ) S - I

I - (A) fs m Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU 5 100 mA 1 S = I m 1 S= 100 mA 106

S= 100 kW = 10 V Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU 6 Rs Rs 50 V Ifs= 500 mA Im Rm=1 kW Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Rs

+ 50 V - Im + Vm - : Ifs= 500 mA Vm = I fs Rm Rm=1 kW = 500mA 1 kW = 0.5 V

I m Rs = 50 V - Vm 50 V - Vm Rs = I fs ( I m = I fs ) 50 V - 0.5 V = 500 mA 49.5 V = 500 10- 6 A = 99 kW 7 Rs1, Rs2, Rs3 Rs1

Rs2 + - Rm=1 kW Rs3 Ifs= 50 mA 10V 3V 30V + Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU 3 V, Rs1 Rs1 + - Rm=1 kW Ifs= 50 mA +3

3 V = I fs ( Rs1 + Rm ) 3V ( Rs1 + Rm ) = I fs V- 3V = 50 mA = 60 kW Rs1 = 60 kW- Rm = 60 kW- 1 kW = 59 kW 10 V, Rs2 Rs2 + - Rm=1 kW

Ifs= 50 mA 10 V = I fs ( Rs 2 + Rm ) 10 V ( Rs 2 + Rm ) = I fs +10 V- 10 V = 50 mA = 200 kW Rs 2 = 200 kW- Rm = 200 kW- 1 kW = 199 kW 30 V, Rs3

Rs3 + - Rm=1 kW Ifs= 50 mA 30 V = I fs ( Rs 3 + Rm ) 30 V ( Rs 3 + Rm ) = I fs +30 V- 30 V = 50 mA = 600 kW Rs 3 = 600 kW- Rm = 600 kW- 1 kW

= 599 kW (Multiple Range 59 kW + - Rm=1 kW 599 kW Ifs= 50 mA 199 kW 10V 3V 30V + - (Universal

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU C Voltmeter Universal Type Rs3 Rs2 Rs1 + - Rm Ifs V3 V2

V1 + - 8 Ra, Rb, Rc Rc Rb Ra 10V 30V 3V + Rm=1 kW Ifs= 50 mA + -

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU 3 V, Ra Ra 3 V = I fs ( Ra + Rm ) + Rm=1 kW Ifs= 50 mA + 3V 3V ( Ra + Rm ) = I fs - 3V

= 50 mA = 60 kW Ra = 60 kW- Rm = 60 kW- 1 kW = 59 kW 10 V, Rb Rb Ra 10 V = I fs ( Ra + Rb + Rm ) + + Rm = 1 kW Ifs

= 50 mA 10 V ( Ra + Rb + Rm ) = - 10 V I fs 10 V = 50 mA = 200 kW Rb = 200 kW- Rm - Ra = 200 kW- 1 kW- 59 kW

= 140 kW 30 V, Rc 30 V = I fs ( Rc + Rb + Ra + Rm ) Rc Rb Ra + + Rm 1 k Ifs 50 mA - ( Rc + Rb + Ra + Rm ) =

- 30 V R c 30 V I fs 30 V = 50 mA = 600 kW = 600 kW- Rm - Rb - Ra = 600 kW- 1 kW- 140 kW- 59 kW = 400 kW (Sensitivity)

3 V Ra + Rm S= V 60 kW = 3V kW = 20 V 10 V Rb + Rm S= V 200 kW

= 10 V kW = 20 V 30 V Rc + Rm S= V 600 kW = 30 V kW = 20 V (Voltmeter Loa

Loading Effect Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU E Ie X

VR1 = I e R1 R1 =E Y X E Im R1 Rm Y E Im = R1 // Rm

VR1 = I m R1 E = R1 R1 // Rm Rs Rs (R ) in Im Rin = Rm + Rs

Ifs= 500 mA Rm Rm=1 kW 9 RB Meter :S =20 kW/V , R =1.5 kW, range = 10 V m E 30V RA= 25 kW RB = 5 kW Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU

Rs RB RB Rs Rs Rm Rs + Rm S= V Rs + Rm = SV k = 20 10 V V = 200 kW Rm = 1.5 kW Rs = 200 kW- Rm

= 200 kW- 1.5 kW = 198.5 kW RB E 30V RA= 25 kW RB = 5 kW RB VRB = E RA + RB (Voltage Divider)

5 kW = 30 V 5 kW+ 25 kW =5 V RB RA= 25 kW E 30V RB = 5 kW RB(new)= R

B RB(new) Rs=198.5 kW =1.5 kW Rm // ( Rs + Rm ) RB ( Rs + Rm ) = RB +( Rs + Rm ) 5k 200k = 5k + 200k = 4.88 kW

RB RB ( new) VRB (new) = E RA + RB ( new) 4.88 kW = 30 V 5 kW+ 4.88 kW = 4.9 V

Xt - Xm % Error = 100 Xt = = 5 V - 4.9 V 100 5A 0.1 V 100 5V = 2%

Loading Effect Rm+Rs > Error Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU +Rs > Error RS Rs Rm 100 k Rm RX (new) 90.91 k X

RS E RX = 1000k Rs Rm 10 k Rm Y RS RX ( new) 9.9 k Rs Rm 1 k Rm RX (new) 0.999 k Ohmmeter

(Ohmmeter) DArsonval Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU (Ohmmeter) 2 - - R% 0.1R%

Ifs Rm 0.9R% E X Y R Ohmmeter RS E Rx

Radj 3 1. 2. () Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU R1 I Rm Rx Im

V R I E R1 ( Rm DArsonval Rx X Y (Open Circuit, R1 I Rm I I m 0

Rx Im E X Y (Short Circuit, R1 I Rm Rx Im E I I m I fs R1 Rm

E RT E X Y ( = 0 < Rx < R1 I Rm Rx Im E E I

R1 Rm Rx RT Rx 0 E X Y ( = 0 < Rx < E I RT Rx E I fs RT

I (Im) Ifs (D) R I E R D I fs T E RT Rx T RT Rx

Rx Rx RT RT D 1 D RT D D

Radj 1k 0 R Rm 2k Ifs Im 5V I fs 3 k 1.67 mA E=5V E 4 V Radj

Radj 1k Radj Rm 2k Ifs Im Radj 0.39 k Rm 2k Ifs E=4V 4V I fs 3 k 4V

2 k 0.39 k 1.67 mA Im 1.33 mA E=4V 10 0.25Ifs, 0.5Ifs, R% 0.75Ifs Ifs=1mA 0.1R% 0.9R% Rm=100Ohm X

E=3V Rx Y Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU Radj Radj Rx = 0 ( D = 1 , Ifs = 1 mA E RT = Radj + Rm = I E = I fs 3V = 1 mA

= 3 kW Radj = 3 kW- Rm = 3 kW- 0.1 kW = 2.9 kW I = 0.25 Ifs D = 0.25 1 D Rx RT D 1- 0.25 = 3 kW

0.25 = 9 kW I = 0.5 Ifs D = 0.5 1 D Rx RT D 1- 0.5 = 3 kW 0.5 = 3 kW I = 0.75 Ifs D = 0.75 1 D

Rx RT D 1- 0.75 = 3 kW 0.75 = 1 kW 9 kW 3 kW 1 kW 11

1.5 V ( R2 ( W = 15 k x R1 10 kW R2 5 kW Rx Rm=1 kW Im=100 mA

E=1.5V 2 ( R1 + R2 + Rm = RT E = I AA Rx = 0 I = 100 Ifs = RT E R2 = - R1 - Rm I fs 1.5 V

= - ( 10 kW) - ( 1 kW) 100 mA = ( 15 kW) - ( 10 kW) - ( 1 kW) = 4 kW 15 k W RT D RT Rx 15k 15k 15k = 0.5 15 kW

12 11 1. R2 ( W = 15 k R1 10 kW R2 5 kW Rm=1 kW Rx Im=100 mA E=1.5V1.1 V

2 ( R1 + R2 + Rm = RT E = I AA Rx = 0 I = 100 Ifs = RT E R2 = - R1 - Rm I fs 1.1 V = - ( 10 kW) - ( 1 kW)

100 mA = ( 11 kW) - ( 10 kW) - ( 1 kW) = 0 kW 15 k W RT D RT Rx 11k 11k 15k = 0.423 1 D

Rx RT D 1 0.423 15k 0.423 = 20.46 kW Im Iadj IT Rm E IT = Rx + R1 +( Radj // Rm )

Vm Radj R1 Rx Radj // Rm << R1 E IT Rx + R1 Vm IT ( Radj // Rm ) Im = = Rm Rm Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU R1 Rx I

Rm Im E Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU 13 kW kW 15k 15 45k 150 5k R1= 14 kW I Rm=1 kW Rx

Im=100 mA E=1.5V Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU R D = 0.5 RT D= RT + Rx RT 0.5 = RT +150kW RT = 150 kW RT = Rm + R1 R1 = RT - Rm = 150 kW- 1 kW

= 149 kW 150k R1=149 kW I Rm=1 kW Rx Im=100 mA E=1.5V 14 15 Ohm R1=14 kW

I Rx R2 Rm=1 kW 15 kW Im=100 mA E=1.5V Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU R1=14 kW I Rx R2 Rm=1 kW 15 kW Im=100 mA

E=1.5V RT R2 // R1 Rm 15 14 k + 1 k 15 + 14 k + 1 k 14.98 15.0 1 D Rx RT D 1 0.5 15 0.5 15

Im D = 0. Rm Vm IT Iadj Radj R3 x 100 R2 x 10 R1 x1 X1

Rh 1 X 10 Rh 10 X 100 Rh 100 Rx A B Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU (Shunt Ohmmete R1 A Rm

E Rx Im S V R I B R1 ( Rm DArsonval Rx (Shunt Ohmmete

Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU X Y (Short Circuit, R1 Rm E I m 0 Im S

X Y (Open Circuit, R1 Rm E Im S E I m I fs R1 Rm E RT

X Y ( = 0 < Rx < R1 I E Rm Im S R1 I E

Rm Rm // Rx Im S Rx E E I Rx Rm R1 Rm // Rx R1 Rx Rm Rx Rx I m

I Rx Rm Rx E Rx Rm R Rx Rm 1 R R x m X Y ( = 0 < Rx < R1 I

E Rm Im S Rx ERx Im R1 Rm Rx Rm Rx 0 X Y ( = 0 < Rx <

ERx Im R1 Rm Rx Rm Rx E I fs RT Im Ifs (D) Im D I fs ERx R1 Rm Rx Rm Rx E R1 Rm

Rx R1 Rm Rx R1 Rm Im D I fs Rx RR Rx 1 m R1 Rm Rx Rx R p - RR (R1 // Rm)

Rx p D - D R R 1 D p x 15 0.25D, 0.5D, R1 0.75D

E 1.5 V Rm= 1 kW Rx Im= 100 mA Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU R1 Rx = ( D = 1 , Ifs = 100 E I m I fs R1 Rm E RT I fs

E RT = 1.5 V 100 mA = 15 kW R1 = 15 kW- Rm = 15 kW- 1 kW = 14 kW I = 0.25 Ifs D = 0.25

Rx D R p 1 D R p R1 // Rm R1 Rm R1 Rm 14 k 1 k 14 k + 1 k 933.33 Rx D R p

1 D 0.25 933.33 1 0.25 311.11 I = 0.5 Ifs D = 0.5 Rx D R p 1 D 0.5 933.33 1 0.5 933.33 I = 0.75 Ifs D = 0.75 Rx D R p

1 D 0.75 933.33 1 0.75 2.8 k 311.11 933.33 2.8 k Im Rs Rm Radj

Rsh1 x1 x 10 Rsh2 Rsh3 IT x 100 E Rx A B Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU

(Standard Resistor, Rs) Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU X Y (Short Circuit, VRm VRAdj E I m I fs X Y (Open Circuit, I m 0

X Y ( = 0 < Rx < IT E Rm RAdj // Rs Rx Rs Im IT Rm RAdj Rs Rs E Im

Rm RAdj Rs Rm RAdj // Rs Rx 16 Rx = 24 R x1 E = 1.5 V 14 kW R1 9.99 kW Rx RS RAdj

2.875 kW Rm= 3.82 kW 10 kW Im= 37.5 mA R1 90 + 900 + 9 k 9.99 k 24 Im Rx = E = 1.5 V 14 kW Rx IT R1 9.99 kW

RS RAdj 2.875 kW Rm= 3.82 kW 10 kW Im= 37.5 mA E IT Rx 14 k R1 RAdj Rm // Rs E 24 14 k 9.99k 2.875k 3.82k //10 31.254 mA Rs Im

IT Rs R1 RAdj Rm 10 31.254 mA 10 16.685 k 18.72 A Im D I fs 18.72 A 37.5 A 0.5 Multimeter

(Multimeter) Piyadanai Pachanapan, 303251 Electrical Instruments & Measurements, EE&CPE, NU nalog Multi-meter RM IM RSH3 RSH2 R1

RSH1 RS1 I3 V1 I2 V2 I1 V3 Rx1 + ( - ) COM RZ RS2 E

RM IM RSH3 RSH2 RSH1 I3 I2 I1 + ( - ) COM RM IM

RSH3 RSH2 RS1 RSH1 I3 V1 I2 V2 I1 V3 Rx1 + ( - ) COM RS2

RM IM RSH3 RSH2 R1 RSH1 Rx1 ( - ) COM RZ E The End

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