# Can a galvanometer measure the voltage?

### The moving coil galvanometer

In many technical and physical applications, measurement of electrical currents is essential. The moving-coil galvanometer is one way of achieving this, although with some effort, but with great precision. It can be used to measure not only currents but also current surges and thus charges. In the following experiments we will often use it to measure magnetic fields.

literature
Wesp (task and appendix, very detailed); Whale (equation of motion, logarithmic decrement; only in older editions); BS-2; Dem-2; NPP; Gifts.

equipment
Figure 3927 shows a photo of the experiment with accessories:
1 moving-coil galvanometer with laser and scale, 3 air coils, 3 plug-in resistors, 3 switches, 2 power supply units (250 V, 2 V), 1 multimeter.

Basics
The construction of a mirror galvanometer

Fig. 4507 Sketch of a galvanometer - setup from above (SVG)

Fig. 4517 Sketch of a (torsion) galvanometer - detailed view (SVG)
Let the magnetic flux density in the air gap be . The for Field perpendicular sides of the coil like the length the other the length . Becomes a (hereinafter positive) voltage applied to the galvanometer coil, the current flows ( is the internal resistance of the galvanometer). Then the Lorentz force acts on the sides of the coil that are perpendicular to the B field

generated, where the coil area and is the galvanometer constant. This torque is offset by several back-driving torques, which are derived in detail in W. Westphal's book. The complete equation of motion of the galvanometer is:

with moment of inertia, Coefficient of air friction , Spring constant (benchmark) and external resistance. By dividing by in the galvanometer equation Eq. (184) we get the well-known equation of motion of a damped oscillation with zero point

The corresponding cases (oscillation, creep, aperiodic borderline case) are to be discussed.

The sensitivity of the galvanometer
The sensitivity of a measuring device is generally understood to be the quotient of the deflection and the measured variable. In the case of the galvanometer, a distinction must be made between current sensitivity, voltage sensitivity and ballistic sensitivity.

Ballistic or shock galvanometer
Charges can be measured by their force effect, by the potential difference or by the current surge that occurs when the charge flows away. An example is the measurement of the deflection of a ballistic galvanometer, which is caused by the current surge when the charge flows through the galvanometer. The duration of the current surge should be less than 1 the period of oscillation of the galvanometer. If a very short current impulse is sent through the galvanometer, the moving coil executes a ballistic or shock deflection analogous to the ballistic pendulum in the mechanics, which is excited by a short force impulse. "Very short" means "very small compared to the period of oscillation T". The moving coil swings from its rest position to a reversal point and then returns, depending on the damping, swinging or creeping back to the equilibrium position. The first reversal point is a measure of the current surge .

execution
The circuit for the implementation and measurement of oscillation, creep and aperiodic borderline cases is shown in Figure 4521. The deflection is reversed by reversing the polarity of the voltage source.

Fig. 4521 Galvanometer circuit 1: Oscillating case, creeping case, borderline case (SVG)

Fig. 4533 Galvanometer circuit 2: Balistic galvanometer (SVG)
Figure 4533 shows the circuit structure for measurements with the ballistic galvanometer.
1. By dividing the voltage (0.10 /10) use the 2 V power supply unit to create a voltage of approx. 2e-5 V and apply it across the series resistor to the galvanometer. Measure the deflections For from 0 - 200 left and right. Please in 20 -Measure steps (22 measured values).
2. In the same circuit, you generate a deflection by applying the voltage. To do this, close the resistance beforehand with switch S2 briefly. After reaching a sufficiently large deflection, open switches S1 and S2 and set different external resistances:
3. Ballistic galvanometer: The primary coil of the air transformer is connected to the power supply unit (0-60 V), the secondary coil via connected to the galvanometer. Opening and closing the primary circuit causes voltage surges in the galvanometer circuit induced. Measure For from 1-10 (10 measured values). Also the amperage is to be measured.
4. Please write down the distance of galvanometer and scale and the required coil data (which data do you need for the evaluation?)
1. Explain the following backdriving moments in the galvanometer: induction moment, frictional moment, straightening moment, moment of inertia.
2. Derive the formula for the moment of induction:

Do you know a technical application of this phenomenon (see experiment "Pohlscher Resonator")?
3. Derive the equation of motion Eq. (184) for the galvanometer.
4. What is the significance of the series resistor ?
5. Why is a galvanometer an ammeter?
6. Please discuss the three cases for the oscillation equation Eq. (185) (with graphics!):
7. Why is the borderline case so important for metrology? It occurs when there is a certain external resistance. Derive the formula for the limit resistance:

How can this best be done for a wide range of external resistances? What applies to the resistance in the case of oscillation or creep??
8. Discuss the sensitivities:
1. [Current sensitivity:]

2. [Voltage sensitivity:]

3. [Ballistic (shock) sensitivity:]

with maximum deflection .
9. How can the current sensitivity be determined from the shock sensitivity?
10. How can charge quantities be measured with a (ballistic) galvanometer?
11. Why can we reduce the equation of motion in the ballistic case as follows:

What follows for the pointer movement ? Derive:

12. be known. Calculate the deflection at the first reversal point .
evaluation
1. Please enter 1 / as a function of and take the current sensitivity from the slope of the straight line and the internal resistance from the intercept of the galvanometer.
2. The decrement is for each oscillation case to calculate (plot reversal points as a function of time semi-logarithmically) and as a function of ) to apply. With the help of relationships:

the galvanometer constant can be derived from the slope and ordinate segment of the straight line , the moment of inertia and the coefficient of air friction be determined.
3. Ballistic galvanometer: please draw . From the limit for please calculate the ballistic sensitivity and check the relationship .
4. Why will smaller for large attenuation?
Remarks
Please note that contact stresses can lead to fluctuations in the zero position of the light pointer during measurements. Therefore, the position should be checked before and after each measurement and the measured value corrected if necessary. The plug-in resistors should all be screwed in correctly before the attempt, especially if they have not been used for a long time, in order to eliminate contact problems caused by oxidation. These resistors are very accurate and robust. When using it, it should be noted that an inserted plug short-circuits the resistor - the corresponding resistor is "deactivated" - and a missing plug "activates" the resistor.