ECE 201 Circuit Theory I 1

Measuring Voltage and Current

• d’Arsenval analog meter movement

ECE 201 Circuit Theory I 2

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 3

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 4

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 5

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 6

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 7

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 8

I20mA

R124

R25.5

Rmeter0.5

2420 16.27

24 5.524

(20 ) 1624 5.5 0.5

16% 1 100% 1 100% 1.66%

16.27

true

measured

measured

true

i mA mA

i mA mA

ierror

i

io

ECE 201 Circuit Theory I 9

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 10

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 11

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 12

What will the voltmeter read?What is the % error in the reading?

(20 )(24 5.5 ) (20 )(4.47 ) 0.089492

(20 )(24 5.5 5000 ) 0.89411

0.89411% 1 100% 1 100% 0.09%

0.89492

true

measured

measured

true

v mA mA V

v mA V

verror

v

I20mA

R124

R25.5

Reffective5k