Transcript Measuring Voltage and Current

Measuring Voltage and Current
• d’Arsenval analog meter movement
ECE 201 Circuit Theory I
1
Analog Ammeter
• Use a d’Arsenval meter movement with a
parallel resistor (shunt).
• The parallel resistor diverts some of the
current away from the meter movement.
ECE 201 Circuit Theory I
2
Analog Voltmeter
• Use a d’Arsenval meter movement in
series with a resistor (multiplier).
• The resistor limits the voltage drop across
the meter movement.
ECE 201 Circuit Theory I
3
Sources of Error
• Any instrument (meter) used to make
measurements extracts energy from the
circuit. (Known as “loading” the circuit).
• The amount of error due to loading
depends on the effective resistance of the
instrument compared with the resistance
in the circuit.
ECE 201 Circuit Theory I
4
Rule of the “one-tenth”
• The effective resistance of the ammeter
should be no more than 1/10th of the value
of the smallest resistance in the circuit.
– The current being measured should be the
same with or without the ammeter.
ECE 201 Circuit Theory I
5
For a Voltmeter
• Since voltage is a parallel measurement,
the “loading” effect is minimized when the
voltmeter resistance is much higher than
the circuit resistance across which the
measurement is being made.
ECE 201 Circuit Theory I
6
Problem # 3.32
• An ammeter with a resistance of 5Ω is
used to measure the current io in the
circuit.
• What is the % error in the measured
value?
ECE 201 Circuit Theory I
7
io
R2
5.5
I
20mA
R1
24
Rmeter
0.5
24
itrue 
 20mA  16.27mA
24  5.5
24
imeasured 
(20mA)  16mA
24  5.5  0.5
 imeasured

 16

%error  
 1  100%  
 1  100%  1.66%
 16.27 
 itrue

ECE 201 Circuit Theory I
8
Problem # 3.33
• A d’Arsenval voltmeter is shown.
Determine the value of Rv for a full-scale
reading of 5 Volts.
ECE 201 Circuit Theory I
9
Choosing the Multiplier Resistor
• When 5V is applied, the meter will be at
full-scale deflection.
• The meter resistance is 50Ω.
• Total resistance needs to be 5kΩ.
• The series resistor Rv (multiplier) needs to
be 4950Ω.
ECE 201 Circuit Theory I
10
Problem # 3.34
• The d’Arsenval voltmeter described in
Problem # 3.33 is used to measure the
voltage across the 24Ω resistor.
ECE 201 Circuit Theory I
11
What will the voltmeter read?
What is the % error in the reading?
I
20mA
R1
24
R2
5.5
Reffective
5k
vtrue  (20mA)(24 5.5)  (20mA)(4.47)  0.089492V
vmeasured  (20mA)(24 5.5 5000)  0.89411V
 vmeasured

 0.89411 
%error  
 1 100%  
 1 100%  0.09%
 0.89492 
 vtrue

ECE 201 Circuit Theory I
12