# Which of the following has higher resistance - milliammeter or ammeter?

The question is the same as the heading - Which of the following has higher resistance - milliammeter or ammeter ?

Now my teacher's and my answers don't match. It is assumed that the spring constant / torsional constant is same for both cases and all other physical constants except the resistance (and/or the specific resistance) (flux, number of loops etc) of the ammeters are same.

The two answers -

1. Milliammeter has lower resistance. Consider a wire carrying 10mA , if we attach an ammeter or a milliammeter to it, the deflection of the ammeter will be much lower than the deflection of milliammeter.

$\phi = (\frac{NAB}{k})\frac{V}{R}$

Since, milliammeter is more sensitive, the resistance is lower in milliammeter.

1. For a constant voltage , the current through a milliammeter must be lower (in the order of milliamperes) but the current through a ammeter would be higher (in the order of amperes) thus the resistance in milliammeter will be higher.
• It depends entirely on the technology. If both use identical D'Arsonval movements the milliammeter will have higher resistance since it will have a greater value shunt resistor (if it has such a resistor at all). If they use equivalent technology D'Arsonval movements then the milliammeter will still have higher resistance, since the length of the armature winding will be longer (and presumably the wire must be thinner as well). But if some electronic technology is used then all bets are off. – Hot Licks Feb 22 '15 at 20:39
• @HotLicks why will it have a higher shunt resistance? – Soham Feb 23 '15 at 7:11
• Because the "shunt" does exactly that -- it shunts current past the meter. To have a higher amp range you shunt more current, which means a smaller-valued shunt resistor. For a lower amp range you have a larger-valued shunt resistor (or no shunt at all). Draw the circuit diagram. – Hot Licks Feb 23 '15 at 12:41
• but you can't decrease the amp range can you ? – Soham Feb 23 '15 at 14:01
• my main doubt is - if the milliammeter has the higer resistance then the relative error in reading would be very high – Soham Feb 23 '15 at 14:03

## 4 Answers

Answer #1 uses an invalid argument. The conclusion that a milliammeter has lower resistance does not follow from the observed fact that the milliammeter has higher deflection.

Consider that some work must be done to deflect the needle. Because of the assumption that the physical constants are the same, the work is equal for equal deflection. Also remember that electrical power is I2R. Since for the same deflection, the current is lower in the milliammeter, the effective resistance must be higher.

But this argument too is in error, because power != force of deflection. Rather power is rate of work per time. The relationship between force and current depends on magnetic field strength, and the connection between that and resistance is very tenuous.

Finally, your question says that the two meters are physically identical in every way. While implies that the resistance is also identical. You can't vary resistance by changing the gage of wire, for example, without also affecting the spring constant.

• i can change the material – Soham Feb 22 '15 at 19:30
• Pretty sure that changes the spring constant also. I guess you can replace both the material and the gage, to get the same spring constant back but with a different resistance. – Ben Voigt Feb 22 '15 at 19:32
• the spring is not necessarily made up of the same material as the conductor – Soham Feb 22 '15 at 19:33
• Are number of loops, etc, held constant only for the movement, and allowed to change on the signal conductor? – Ben Voigt Feb 22 '15 at 19:34
• what is signal conductor? – Soham Feb 22 '15 at 20:28

I don't have the facilities at hand to draw a circuit diagram, so I'll just describe it. A conventional electromechanical current meter consists of these parts:

1. M1 -- the meter movement itself (which we idealize as having zero internal resistance).
2. R1 -- the innate resistance of the meter movement. This is packaged inside the meter, but we can consider it to behave like a separate discrete resistor.
3. R2 -- the external (to the meter movement) series resistor. This is not absolutely necessary, but most designs have one.
4. R3 -- the "shunt" resistor

M1, R1, and R2 are wired "in series". And, for our purposes, we can consider R1 and R2 as a single resistor. R3 is wired "in parallel" with the other three.

So assume that M1's needle registers full scale when 100ma is running through the meter -- this means that M1 is a "100ma movement". Also assume that R1+R2 sums to 10 ohms. This means that if we apply 1 volt to the meter (with R3 not present), 100ma will flow through the 10 ohms of resistance, and the meter will register full scale.

Now, suppose we want a meter that reads 10A full scale. This means that when 10A is flowing through the meter assembly, 100ma must be flowing through the meter proper, while 9.9A flows through the "shunt" resistor. The easy way to figure it is that 1V will produce a full scale reading on the meter, so we need a total resistance that will pass 10A at 1V. Ie, the total resistance of the meter assembly must be 0.1 ohm, and 9.9A must flow through the shunt resistor at 1V. So the shunt resistor would be (1.0 / 9.9) or 0.10101... ohms.

So, clearly the milliammeter has a higher resistance (100 ohm) than the ammeter (0.1 ohm).

• shunt should be parallel to R1 only, isn't it ? – Soham Feb 24 '15 at 5:06
• @LucyferZedd - No, you regard R1 as being internal to the meter movement, and treat M1, R1, and R2 as being together. If you put the shunt just across R1 (and not the meter proper) then 10A would blow up the meter, since it's designed for 100ma max, not 10A. Draw a picture. – Hot Licks Feb 24 '15 at 12:53

Let us assume that the instrument design is the same as in http://en.wikipedia.org/wiki/Ammeter (the words "spring constant / torsional constant", "flux, number of loops" seem to imply that). Then, to get the same deflection for lower current you need more loops, therefore, the resistance of the milliammeter will be higher. It looks like the same conclusion is correct for designs with shunts, but the analysis is trickier.

• what if the material is different? – Soham Feb 22 '15 at 19:42
• @Lucyfer Zedd: you assume that "all other physical constants except the resistance (flux, number of loops etc) of the ammeters are same". – akhmeteli Feb 22 '15 at 20:05
• @Lucifer Zedd: I am not sure if I have interpreted your question correctly. I assumed that resistance, flux, and number of loops could be different, so you add more loops thus adding resistance and flux. Was I wrong? – akhmeteli Feb 22 '15 at 20:12
• oh yes , i've edited a bit – Soham Feb 22 '15 at 20:28
• @Lucyfer Zed: I guess you can always make an ammeter and a milliammeter in such a way that the former will have lower resistance, but maybe we should discuss a general trend, rather than exceptions. – akhmeteli Feb 22 '15 at 20:37

The ideal current meter has 0 resistance, which means it drops 0 volts regardless of how much current you put thru it. Real current meters have some resistance. One measure of quality of a current meter is how low this resistance is, with lower being better since that disturbs the system being measured less.

At one level, your distinction between "ammeter" and "milliammeter" is meaningless. They are both current meters, just reading out the measured value in different units. This is like asking which is longer, a foot tape measure or a meter tape measure.

However, we can assume or guess from the labels that the milliammeter is intended to measure lower currents than the ammeter. Since the electronics for amplifying and converting the small voltage across the sense resistor are the same at the same level of quality, the milliammeter will have a larger sense resistor. This is needed to generate the same voltage at milliamp levels that the sense resistor in the ammeter does at ampere levels.

Again, there is no inherent rule that all current meters intended for milliamp-level currents have larger sense resistors than those intended for ampere-level currents, but that will generally be the case when the two meters have about the same level of technology and price. There are also other ways of measuring current than measuring the voltage drop across a sense resistor, but that is by far the most common for a off the shelf "ammeter".

• Whoever downvoted this, I'd really like to know what you think is wrong, misleading, or badly written. – Olin Lathrop Jul 15 '16 at 23:34

## protected by Qmechanic♦May 30 '15 at 13:26

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