Purpose: The purpose of this experiment is to take a galvanometer and design circuits to match that enables one to measure current and voltage of an arbitrarily selected range.

Theory

The Ammeter and the Voltmeter

The majority of electrical measurements is concerned with determining the magnitudes of currents and voltages. Electrical currents are commonly measured with ammeters and voltages with voltmeters. These instruments are delicate and may be easily damaged if they are connected improperly in a circuit. Also, the internal resistances of meters may add appreciable error to measurements in some cases. Hence, it is important to understand the basic principles of their operations.

The basic component of both ammeters and voltmeters is the galvanometer. The galvanometer is an electromagnetic device capable of detecting very small electrical currents. In this experiment, the characteristics of a galvanometer and the basic construction of the ammeter and voltmeter will be investigated.

The basic design of a moving-coil galvanometer is shown in Figure 1. It consists of a coil of wire on an iron core that is pivoted on bearings between the poles of a permanent magnet. When a current passes through the coil, it experiences a torque and rotates, moving a dial pointer. A balancing counter torque is supplied by control springs. When the coil reaches an equilibrium position, the two opposing torques are equal, and the deflection of the pointer is proportional to the current in the coil.

The scale of a galvanometer is commonly marked with intervals on both sides of a central zero. When the coil current is in one direction, the pointer needle is deflected to the right. If the polarity, and hence the current, are reversed, the needle is deflected to the left. The galvanometer is capable of detecting currents in the micro ampere (mA) range, and the scale graduations give relative magnitudes of the current.

For absolute current values, the current sensitivity of a specific instrument must be known. The current sensitivity is usually expressed in micro amperes per scale division. The number of scale divisions n indicated by the pointer deflection is proportional to the current I_g in the galvanometer coil:

Eq. 1                    Ig  or Ig = kn

where k is the current sensitivity in micro amperes per scale division. As can be seen from the equation, the smaller k, the greater the sensitivity of the galvanometer (greater deflection for a given current).

The galvanometer coil has a resistance r and the current in the coil is also given by Ohm's law:

Eq. 2                         Ig = V/r 

where V is the voltage across the galvanometer. As such a galvanometer could be calibrated in micro amps and used as a microammeter. However, this meter would not be useful in circuits in which the current exceeded the microamp range. Using such a meter in a circuit with a much larger current than that required for full-scale deflection would "peg" the needle, causing possible damage to the mechanism. Also, a large current would heat the coil and would eventually burn out the meter. Thus, a different design is required for a practical ammeter capable of reading current magnitudes in the ampere range.

The dc Ammeter

	To convert a galvanometer to an ammeter capable of reading currents in the ampere range, a small "shunt" resister Rs, is placed in parallel with the galvanometer. This provides an alternate path whereby a large current I can bypass or "shunt" the galvanometer. The resistor r symbolizes the internal resistance of the galvanometer itself.
Figure 2 The Ammeter

An ammeter is always connected in line or in series with a circuit component to measure the current flowing through the component. If an ammeter were connected in parallel with a circuit component having appreciable resistance, the meter would carry most of the current and could burn out.

Since the voltages across the galvanometer and the shunt resistor are equal, we have

or by Ohm's law, I_gr = I_sR_s. Then, in terms of the total current I = I_g + I_s,

and

Eq. 3                         Ig = RsI/(r + Rs)  

and with Eq. 1 we have

Eq. 4                    Ig = kn = RsI/(r + Rs)

The resistance of the ammeter, or the total equivalent resistance of the parallel galvanometer and R_s branch, is very small and usually may be considered negligible relative to resistance R. Hence, to a good approximation, the total current I in the circuit is given by

Eq. 5                          I = V/R

The dc Voltmeter

To convert a galvanometer to a voltmeter that is capable of reading voltages in excess of the microvolt range, a large multiplier resistance Rm is placed in series with the galvanometer as in Figure 3. In this arrangement the voltage drop across the galvanometer branch is Eq.  6                     V = Vg + Vm   and most of the voltage drop across the voltmeter is across the multiplier resistance and not the galvanometer coil. Because of the large internal resistance of a voltmeter, it draws little current from the main circuit.

Figure 3

A voltmeter is always connected in parallel with a circuit component to measure the potential difference or voltage drop across the component. If a voltmeter were connected in series, it would reduce the current in the circuit and the voltage drop across the component.

Then, by Ohm's law,

Eq. 7                 V = kn(r + Rm) or Rm = V/kn - r 

which is also equal to the voltage drop across R, since the galvanometer branch and R are in parallel. Hence, by varying the applied voltage, the galvanometer scale can be calibrated in terms of voltage instead of current.

It can be seen from the preceding discussion that the critical parameters in calibrating a galvanometer as an ammeter or voltmeter are its current sensitivity k or its full-scale current I_g = kn and the coil resistance r. When these quantities are known, the appropriate resistances for full-scale deflection magnitudes I_max and V_max can be found from Equations 4 and 6 respectively. Lower values of current and voltage on these scales are directly proportional to the scale divisions n.

Procedure

Connect the Following Circuit Elements in Series

• Long red lead with fuse from Power Amplifier to Galvanometer
• Medium black lead from Galvanometer to Switch
• Medium black lead from Switch to Resistor Box

  Set Resistor Box (R₁) as follows: 100K dial to zero, the rest all the way clockwise.

• Medium black lead from Resistor Box to Power Amplifier

Figure 4

Setting the Power Supply

• Open Science Workshop
• Connect the annalog plug to "A"
• Select Power Amplifier
• Set the Signal Generator DC 10 V

Testing the Power Amplifier

Finding the Galvanometer Characteristics

R1 for full scale deflection =	_____

Open the switch.

Leave the circuit as is, including the value of R1.

Connect the other resistance box (Rs) in parallel with the galvanometer as shown in Figure 5.

Figure 5

Close the switch and adjust Rs until the galvanometer reads exactly half full scale deflection (If full scale was 50, you need 25). Record this value of Rs as your galvanometer resistance r.

Galvanometer Resistance (r) =	_____

Using the Galvanometer to design a Voltmeter