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
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 fullscale 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?
(10 mA)
Rm
(1 mA,
50 mV)
50 mV/1mA=50 Ohms
50 Ohms in parallel with RA (which is 50/9 Ohms) gives 5 Ohm.
Example 3.5 (b)
• A 50 mV, 1 mA d’Arsoval movement is
to be used in an ammeter with a fullscale 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 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.
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.
+
+
(150 V)
-
1 mA
-
50 mV
Needle resistance: 50 mV/1mA=50 Ohms
Example 3.6 (c)
• How much resistance does the 150 V
meter insert into the circuit?
+
+
(150 V)
Rm
-
1 mA
-
50 mV
Rv=149,950 Ohms, Rm=Rv+50mV/1mA=150,000 KOhms
Accuracy of Multimeter
• Analog multimeters: 3%
• Portable Digital Multimeter: 0.5 %
• Wheatstone: 0.1 %
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
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 b
i1=i3
I2=ix
Relationship:
VR1=VR2
VR3=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 do
with this resistive
network? Can you simplify it?
Δ to Y Equivalent Circuit