Physics 271L Exp 4

## Physics 271L Experiment 4

#### [ Voltmeter | Ammeter | Procedure | Questions ]

Purpose: To Design and Construct a Voltmeter and an Ammeter

Before designing a voltmeter or ammeter from a galvanometer it is necessary to determine the resistance of the galvanometer, Rg, and the value of the current which causes the galvanometer to read full scale, I f . These values are often stamped on the galvanometer by the manufacturer. We shall find Rg using the half deflection method and the circuit in Fig. 1. BE VERY CAREFUL NOT TO PASS TOO LARGE A CURRENT THROUGH THE GALVANOMETER . Before plugging the line cord in, set R1 = 25,000 and R2 = 1 . Turn on the current and adjust R1 to produce a full scale deflection on the galvanometer with S3 open. Then close S3 and adjust R2 until you obtain a half-scale deflection. If R1 >> R2 then Rg R2 . If R1 is not much greater than R2 this approximation is not good. You will get best results if the voltage divider is set to give maximum voltage to the circuit and R1 >> R2 to begin with. If the slide wire gets to end A and you still do not have full scale current in the galvanometer TURN OFF the current and start over with a reduced value of R1 (8000 ). The full scale current of the galvanometer is read directly from the ammeter when S3 is open. For this determination use the 15mA scale of theVOM for the ammeter.

Design of a Voltmeter

In addition to determining Rg and I f  you must also select a voltage V which you wish to cause a full-scale deflection. This is your choice, determined by the intended use of the voltmeter. The only restriction of V is that it must be greater than or equal to If Rg (Why?)

The voltmeter is constructed by wiring a resistor R in series with the galvanometer as shown in Fig. 2.

When the potential difference between the voltmeter terminals T1 and T2 is V, the current through G must be If . Summing the voltage drops across R and Rg, in this case, gives

V = If R +If Rg

This can be solved for R to yield

R = V/If - Rg

#### [ Purpose|Procedure|Questions| Top ofPage]

Design of an Ammeter

1. Just as it was necessary to choose a full-scale voltage for the voltmeter so it is necessary to select a current I which you wish to cause a full-scale deflection. Again this choice is based on the intended use of the ammeter and is limited only by the condition I > If . (Why?) The ammeter is constructed by wiring a resistor R, called a shunt, in parallel with the galvanometer as shown in Fig. 3.

When the current I is in the ammeter, you want If as the current through the galvanometer and, by subtraction, I-If through R. Since the voltage drop across Rg must be the same as the voltage drop across R(Why?), the following equation holds.

If Rg = (I-If)R or R = If Rg/(I - If)

2. Ayrton Shunt Method. Sometimes a shunt resistance needed is too low for the resistances actually available (e.g. need 0.007 , but only have 1 ). The lowest available resistance can be used as Rx , but another resistance, Ry , must be put in series with Rg to protect the galvanometer. Generally, if Rx is used,then Ry should be: Ry = ([I/If] -1)Rx -Rg

#### [Purpose|Volmeter|Questions|Top ofPage]

Procedure:

• a. Construct the circuit shown in Figure 1 to determineIf and Rg . After you have done so, do not do anything until your instructor verifies your values are correct by watching you make your measurements again.

• b. Next, construct the circuit in Figure 2 to convert the galvanometer to a 0-20V voltmeter. Measure voltages of about 4, 8, 12V and compare the readings on the constructed meter with those of the commercial voltmeter connected between the same points. (See figure 2).

• c. Convert the galvanometer to a 0-10.0mA ammeter. Construct the circuit of Figure 3. Compare the readings for your constructed ammeter to those of the commercial ammeter.

• d. To construct a meter which will measure a current I of 1.0 A , follow the circuit in Fig. 4 and pick a value for Rx which is easily available, namely, a standard resistor for Rx = 1.0 . Now you calculate the value of Ry on a decade box and place it in series with your galvanometer. Place your meter in a reconstructed circuit of Figure 3. Check the reading of the two meters. Set the decade box initially at 8000 and reduce gradually, comparing the currents on the two meters.

Questions:

• 1. How is a multirange voltmeter internally constructed (like the VOM you have been using)? Draw a diagram and make calculations for 2 V, 20 V, 50 V, and 100V ranges, if If = 1mA and Rg = 20 .

• 2. How is the internal resistance of the multivoltmeter changed as the selected full-scale voltage V is increased? Is this a desirable change, knowing an ideal voltmeter is to have very, very high resistance?

• 3. How is a multirange ammeter constructed? Draw a diagram and make calculations for 0.05 A, 0.10 A, 0.5 A, and 1.0 A ranges, if If = 1mA and Rg = 20 .

• 4. How is the internal resistance of a multirange ammeter changed as the selected full-scale current I is increased? Is this a desirable change, knowing that an ideal ammeter should have almost no resistance?

• 5. What practical difficulties arise in constructing meters having large current ranges? How are these difficulties helped with the Ayrton shunt?

• 6. Derive the expression for the value Ry of the Ayrton shunt.