Lecture 5

Current/Voltage MeasurementResistance 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

RA 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 RA.(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 Ohms50 Ohms in parallel with RA (which is 50/9 Ohms) gives 5 Ohm.

Rm

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?

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 Ohms50 Ohms in parallel with RA (which is 50/999 Ohms) gives 50 mOhm.

Rm

A DC Voltmeter Circuit

RV 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 RV.

1 mA

+

-50 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

+

-50 mV

+

-

(150 V)

Rv=149,950 Ohms, Rm=Rv+50mV/1mA=150,000 KOhms

Rm

Accuracy of Multimeter

• Analog multimeters: 3%• Portable Digital Multimeter: 0.5 %• Wheatstone: 0.1 %

Resistance Measurement

R1,R2, and R3 are known resistorsRx is the unknown resistorAdjust R3 until there is no current in the meter

Wheastone BridgeUsed to measureResistance between1 Ohms and 1 MOhms

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

Derivation

No current from a to bi1=i3I2=ixRelationship:VR1=VR2VR3=VRx

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

Meter Resistance Included

What do you dowith this resistivenetwork? Can you simplify it?

Δ to Y Equivalent Circuit