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Lecture 5

Lecture 5. Current/Voltage Measurement Resistance Measurement Wheatone Circuit. Current/Voltage Measurement. Circuit Model for ideal ammeter/voltmeter. An ideal ammeter has an equivalent resistance of 0 Ohm. An ideal voltmeter has an infinite equivalent resistance. d’Arsonval meter.

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Lecture 5

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  1. Lecture 5 Current/Voltage Measurement Resistance Measurement Wheatone Circuit

  2. Current/Voltage Measurement

  3. Circuit Model for ideal ammeter/voltmeter An ideal ammeter has an equivalent resistance of 0 Ohm. An ideal voltmeter has an infinite equivalent resistance.

  4. d’Arsonval meter When current flows in the coil, it creates a torque on the coil, causing it to rotate and move a pointer across a calibrated scale. The deflection of the pointer is proportional to the current

  5. Commercial Rating • Rating: 50 mV and 1mA • Interpretation: When the coil is carry 1 mA, the voltage drop across the coil is 50 mV and the pointer is deflected to its full-scale position.

  6. A DC Ammeter Circuit RAis added limits the amount of current in the coil.

  7. Example 3.5 (a) • A 50 mV, 1 mA d’Arsoval movement is to be used in an ammeter with a full-scale reading of 10 mA. Determine RA. (10 mA) (1 mA, 50 mV) Current through RA?

  8. Example 3.5 (c) • How much resistance is added to the circuit when the 10 mA ammeter is inserted to measure current? (10 mA) (1 mA, 50 mV) Rm 50 mV/1mA=50 Ohms 50 Ohms in parallel with RA (which is 50/9 Ohms) gives 5 Ohm.

  9. Example 3.5 (b) • A 50 mV, 1 mA d’Arsoval movement is to be used in an ammeter with a full-scale reading of 1 A. Determine RA. (1 A) (1 mA, 50 mV) Current through RA?

  10. Example 3.5 (b) • How much resistance is added to the circuit when the 1 A ammeter is inserted to measure current? (1 A) (1 mA, 50 mV) Rm 50 mV/1mA=50 Ohms 50 Ohms in parallel with RA (which is 50/999 Ohms) gives 50 mOhm.

  11. A DC Voltmeter Circuit RVis added limits the voltage drop across the meter’s coil.

  12. Example 3.6 • A 50 mV, 1 mA d’Arsoval movement is to be used in a voltmeter in which the full-scale reading is 150 V. Determine RV. + + (150 V) - 50 mV - 1 mA Needle resistance: 50 mV/1mA=50 Ohms

  13. Example 3.6 (c) • How much resistance does the 150 V meter insert into the circuit? + + (150 V) 50 mV - - 1 mA Rm Rv=149,950 Ohms, Rm=Rv+50mV/1mA=150,000 KOhms

  14. Accuracy of Multimeter • Analog multimeters: 3% • Portable Digital Multimeter: 0.5 % • Wheatstone: 0.1 %

  15. Resistance Measurement Wheastone Bridge Used to measure Resistance between 1 Ohms and 1 MOhms R1,R2, and R3 are known resistors Rx is the unknown resistor Adjust R3 until there is no current in the meter

  16. Determine Rx • Adjust the variable resistor R3 until there is no current in the galvanometer. • Calculate the unknown resistor from the simple expression: • Rx=(R2/R1)R3

  17. Derivation No current from a to b i1=i3 I2=ix Relationship: VR1=VR2 VR3=VRx

  18. Possible Range of Rx • Rx=(R2/R1)R3 • Change R2/R1 in order to measure a wide range of Rx • Implement R2 and R1 using precision R1, R2 that can be switched into the bridge circuit. Possible values: 1,10, 100, 1000 Ohms • Range of R2/R1: 0.001 to 1000 • Range of R3 usually from 1 to 10 Kohms • Measurable Rx is from1 Ohm to 1 MOhm

  19. Meter Resistance Included What do you do with this resistive network? Can you simplify it?

  20. Δ to Y Equivalent Circuit

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