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 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

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.

A DC Ammeter Circuit R A is added limits the amount of current in the coil.

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 R A. (10 mA) (1 mA, 50 mV) Current through RA?

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

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 R A. (1 A) (1 mA, 50 mV) Current through RA?

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

A DC Voltmeter Circuit R V is added limits the voltage drop across the meter’s coil.

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 R V. 1 mA mV + - (150 V) Needle resistance: 50 mV/1mA=50 Ohms

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

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

Resistance Measurement R 1,R 2, and R 3 are known resistors R x is the unknown resistor Adjust R 3 until there is no current in the meter Wheastone Bridge Used to measure Resistance between 1 Ohms and 1 MOhms

Determine R x Adjust the variable resistor R 3 until there is no current in the galvanometer. Calculate the unknown resistor from the simple expression: – R x =(R 2 /R 1 )R 3

Derivation No current from a to b i 1 =i 3 I 2 =i x Relationship: VR1=VR2 VR3=VRx

Possible Range of Rx R x =(R 2 /R 1 )R 3 – 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: to 1000 – Range of R3 usually from 1 to 10 Kohms – Measurable Rx is from1 Ohm to 1 MOhm

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

Δ to Y Equivalent Circuit