14 Current and Voltage Measurements

7/28/2019 14 Current and Voltage Measurements

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Current and Voltage Measurements

Current measurement

According to current continuity (i.e. charge

conservation) law, the current can be measured

in any portion of a single loop circuit.

VB

Circuit

Element

I

I


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Contact-less methods

VB

I

I

Any current produces a magnetic field.

Magnetic field rotates the indicator

(like a compass needle)

Issues: Not very accurate. Low-sensitive only applicable to high-current circuits


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Current measurement device Ammeter

Magneto-electric ammeter

The ammeter uses the magnetic field created by the current to deflect the needle.

The coil attached to the needle increases the magnetic field of the current.


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The magnetic field of the coil is proportional to the electric current The deflection angle is proportional to the magnetic field

Hence, the deflection angle is proportional to the current

The maximum current that can be measured depends on

the full scale deflection (f.s.d) of the ammeter

Current measurement device - Ammeter


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On a circuit diagrams, an ammeter is shown as an A in a circle.

Current measurement device - Ammeter

AmmeterA


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Series resistance method

most commonly used in all modern instruments

VB

Circuit

ElementX

I

I

1. Break the circuit (or a branch)

2. Insert an ammeter

3. The current through the ammeteris measured by the needle deflection

angle.

5. Electronic instruments are used to

display or transmit the results

4. The current through the resistoror any circuit component X is the

same as that through the ammeter

AmmeterA


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VB

R

I

I

The ammeter inserted in the circuit

changes the actual current in it.

Let the resistance of the Element

X be

R

The actual circuit current is

I = VB/R

After insertion of the ammeter, thetotal circuit resistance changes and

so does the current.

Distortions introduced by Measurement

AmmeterA

The resistor R is shown by

rectangle here to emphasize that

the method can be applied to

ANY circuit component, not to

resistors only.


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Reminder: Series electric circuit

For the resistor 1: I1 = V1/R1;

For the resistor 2: I2 = V2/R2;

From the current continuity:

I1 = I2 = I;V1 = I R1; V2 = I R2 (1)

From the energy conservation:

VB = V1 + V2; (2)

From (1) and (2):

VB = I R1 + I R2 = I (R1+R2) (3)

R1

R2

VB

I

V2

V1

21 RR

VI B

+=

Find V1 and V2 from (1)Solve (3) for the current

21

2

2

21

1

21

111

RR

R

VV

RR

RV

RR

VRRIV

B

B

B

+=

+=

+==


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Distortions introduced by current measurement

VB

Circuit

Element R

I

I


The measured current,

IRR

VI

A

BM


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Problem 1

0

of

40

The resistor 2 kOhm is connected to a 9Vbattery. The Ammeter connected in series withthe resistor indicates the current 4 mA flowingthrough the circuit.

What is the actual current in the originalcircuit (without the ammeter) in mA?

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VB

Circuit

Element R

I

IAmmeterA

Timed response


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Problem 2

0

of

40

The resistor 2 kOhm is connected to a 9Vbattery. The Ammeter connected in series withthe resistor indicates the current4 mA flowing through the circuit.

What is the Ammeter internal resistancein Ohms?

120120

VB

Circuit

Element R

I

IAmmeterA

Timed response


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Problem 3

0

of

40

A resistor is connected to a 9V battery. TheAmmeter connected in series with the resistorindicates the current 4.5 mA in the circuit.The Ammeter internal resistance is 100 Ohm.

What is the actual current in the circuit(without the ammeter) in mA?

120120

VB

Circuit

Element R

I

IAmmeterA

Timed response


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Distortions introduced by current measurement

VB

Circuit

Element R

I

I

The actual / measured current ratio

R

R

R

RR

RR

V

R

V

I

I AA

A

BB

M

+=+

=

+= 1/

R

R

I

I

I

II

I

I A

MM

M

M

=

=

1

AmmeterA


The measured current

The relative measurement error

R

VI B=

IRR

VI

A

BM

=> R

VMM R

R

V

V

V

V==

1


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Voltmeter and ammeter comparison

AmmeterA

The ammeter resistance

RA must be much lower

than the resistance R ofthe circuit to be measured

VoltmeterV

The voltmeter resistance

RV must be much higher

than the resistance R ofthe circuit to be measured

VoltmeterV

Ammeter connected to a large series resistor can be used as a voltmeter

AmmeterA


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Summary

For accurate current measurements, the resistance of the

current meter (connected in series with the circuit element under

testing), must be much smaller than that of the tested element.

For accurate voltage measurements, the resistance of the

voltmeter (connected in parallel with the circuit element under

testing), must be much greater than that of the tested element. The current and voltage measurement errors (relative) are given by:

VMM R

R

V

V

V

V==

1

R

R

I

I

I

I A

MM

=

1


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Smart voltmeter circuit zero current consumption

14 Current and Voltage Measurements

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