**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, **R _{g}**,
and the value of the current which causes the galvanometer to read full scale,

**Design of a Voltmeter**

In addition to determining **R _{g}**
and

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 **T _{1}** and

**V = I _{f } R +I_{f} R_{g}**

This can be solved for **R** to yield

**R = V/I _{f} - R_{g}**

**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 **> **I _{f}**
. (Why?) The ammeter is constructed by wiring a resistor

When the current **I **is
in the ammeter, you want** I _{f}**
as the current through the galvanometer and, by subtraction,

**I _{f} R_{g} =
(I-I_{f})R or R = I_{f} R_{g}/(I - I_{f})**

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 **R _{x}**
, but another resistance,

**Procedure:**

- a. Construct the circuit shown in Figure 1 to determine
**I**and_{f}**R**. After you have done so, do not do anything until your instructor verifies your values are correct by watching you make your measurements again._{g}

- 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**R**which is easily available, namely, a standard resistor for_{x}**R**_{x}**= 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**I**_{f}**=****1mA**and**R**._{g}= 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**I**and_{f}= 1mA**R**._{g}= 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
**R**of the Ayrton shunt._{y}