# Conversion of a Galvanometer to Ammeter and Voltmeter?

I am in 12th std and while reading my Physics textbook I came across a topic called "Conversion of a Galvanometer to Ammeter and Voltmeter." So I read it and found that to convert a Galvanometer to Ammeter we connect a very low value resistance in parallel to the Galvanometer and to convert it to Voltmeter we connect a very high value resistance in series with the Galvanometer.

Now my question is: What is the logic behind this type of conversion? I mean that why the low resistance is connected in parallel to the Galvanometer? Why can we not connect in series? Or why does it have to be low, why can't it be high?

A "moving coil" galvanometer shows a deflection proportional to current flowing through its coil due to very small voltages placed across its terminals.

Full scale deflection of a galvanometer typically requires between tens and hundreds of microamperes, corresponding to a voltage of tens of millivolts across the terminals. The coil resistance of a galvanometer is typically a few Ohms to a few hundred Ohms. Typical full-scale

For the sake of this explanation, let us assume a very sensitive galvanometer with 100 Ohm coil resistance, and 100 microAmperes current for full-scale deflection. Thus, by Ohms Law, the full-scale deflection will require 10 mV across the terminals.

To create an ammeter with a maximum current rating of 1 Ampere, this current must generate 10 mV across a "load resistor" or "shunt resistor". By permitting 1 Ampere to flow through a 10 milliOhm resistor, 10 mV is generated across this resistor. That's perfect for our purposes, so we connect the galvanometer across (in parallel with) this 10 milliOhm resistor:

simulate this circuit – Schematic created using CircuitLab

As the galvanometer's resistance (100 Ohms) is much much greater than the shunt resistance (10 mOhm), we can pretty much disregard the effect of paralleling the galvanometer's coil to our shunt. Thus, in effect the Ammeter we have created, has 10 milliOhms of resistance, which is pretty much negligible, and reads up to 1 Ampere current.

Now for a voltmeter. If we needed a full-scale reading of, say, 20 Volts, we would need to ensure that 20 Volts would cause 100 microamperes (assumption stated earlier) to flow through the galvanometer.

Ohms Law tells us that a resistor of 200 KOhms would pass 100 microAmperes through it, if exposed to 20 Volts. If we were to put our galvanometer in series with this current path, we'd have an excellent 20-Volt Voltmeter. In this case, again, the 100 Ohm coil resistance is negligible in comparison to the 200 KOhm resistor, so we can ignore it.

simulate this circuit

Note that in this case too, the galvanometer is illustrated as a current meter - because that is what it remains. The combination of the galvo, and the 200 K resistor in series with it, provides us a voltmeter that meets our requirements.

The above examples are extreme cases: Measurement of a small maximum current of say 1 milliAmperes instead of 1 A would require the current to pass through a resistance of 10 Ohms (to generate the 10 mV needed by the galvanometer coil). As this is a significant value comparable to the galvo's coil resistance, the actual shunt resistance value calculation would need to take the parallel 100 Ohms (coil) into account.

Similarly, for measuring small voltages by using our galvo as a voltmeter, the series resistor calculation would need to subtract the coil resistance value.

I am sure your textbook explains these calculations in greater detail.

Think about how they are used. A voltmeter is put in parallel across two points under test. In the ideal case, no current flows through the meter. An ammeter is put in series. with the current under test flowing through it. In the ideal case, the ammeter has 0 resistance, else it affects the measurement. If you make the voltmeter low impedance and the ammeter high impedance, it will give bad results.

A galvanometer acts like an ideal ammeter in series with a moderately small resistance. A full-scale reading will require a relatively small amount of current; when that much current is flowing through the meter, it will drop a certain amount of voltage. If a particular meter read full-scale with 100uA, and dropped 0.01 volts with that much current, one could use it directly as an ammeter for reading currents up to 100uA, or as a voltmeter for voltages up to 0.01 volts, but many real-world applications require reading higher currents or voltages.

To read a higher current, it's necessary to add a resistor which can divert most of the current being measured around the meter, so that when the desired full-scale amount of current is flowing through the combination of resistor and meter, the amount flowing through the meter (rather than the resistor) will be 100uA. To scale things up by a factor of N, the parallel resistance should be the resistance of the meter divided by (N-1).

To read a higher voltage, it's necessary to add a resistor which can drop voltage in addition to that dropped by the meter, so that when the desired full-scale voltage is applied, the amount of voltage dropped in the meter will be 0.01 volts. To scale things up by a factor of N, the series resistance should be the resistance of the meter multiplied by N-1.

Incidentally, if one has a precision voltage source, potentiometer, and some precision resistors, there's an even more accurate approach for making measurements using a galvanometer with only a single mark on its scale: use the voltage source and potentiometer to generate an adjustable voltage reference, and use the galvanometer to show the difference between that reference and the voltage to be measured. Adjust the potentiometer until the galvanometer reads zero; the potentiometer's resistance ratio will indicate the ratio of the voltage being measured to the precision voltage source; a good potentiometer will allow that ratio to be measured to three significant figures--much better precision than would be obtained by reading a meter needle.

It is very easy to destroy a galvanometer and I ruined more than a few in my lab days. The basic galvanometer movement requires very little current to deflect the needle to full scale. If you connect your galvanometer to the terminals of a power supply like a battery of lab supply, you will melt the windings or start a fire or see a little flash of light or smell something that is way too hot. I think I have done all those.

But you want to measure a larger current. What to do? What if you could make most of the current flow around the galvanometer? You can, as explained by @Anindo, give the current a path with much lower resistance than the galvo coil. Most of the current will flow through the low resistance path. The low resistance path is called a "shunt" and you can find them on eBay for huge currents or in physics labs that have not been cleaned out of all the "old" stuff. (The eBay ones are meant to be used with a high impedance voltmeter or ADC in a microprocessor, but you can calculate how they will work with a galvanometer). It seems odd, but in essence you can use the galvo to measure the voltage drop on the shunt.

If you want to measure a high voltage, you need a way to limit the voltage across the galvo and thus the current. I high series resistance will cause most of the voltage to drop across the resistor and keep the galvo in a safe range.

Look up "ballistic galvanometer" to see an interesting device.

As ammeter measure current so for its accuracy resistance has to be low so we connect small resistance in parallel with galvanometer to reduce its resistance same as for voltmeter as it measure voltage drop whose value increases as resistance increases so we connect resistance in series with galvanometer