Design a multirange voltmeter capable of full-scale deflection for 20.0 V, 50.0 V, and 100 V . A

Design a multirange voltmeter capable of full-scale...

Key Concepts

Multirange Voltmeter Design

Multirange voltmeter design involves the use of different series resistors to allow the same basic meter movement to be used across various voltage measurement scales. By carefully selecting the resistor values based on the desired full-scale voltage and the known full-scale deflection current of the galvanometer, the instrument can accurately measure multiple voltage ranges.

Series Resistor in Voltmeters

A series resistor is added to the galvanometer to extend its measurement range. By placing a resistor in series, the voltage drop across the combination can be scaled such that the meter only experiences its full-scale deflection current when the maximum voltage of the selected range is applied. This adjustment is crucial for accurately converting the galvanometer into a voltmeter.

Ohm's Law

Ohm’s Law, expressed as V = IR, is a foundational principle in electrical circuit analysis that relates voltage (V), current (I), and resistance (R). In the design of voltmeters, Ohm’s Law is used to calculate the required series resistor that limits the current through the galvanometer to its full-scale deflection value.

Full-Scale Deflection

Full-scale deflection refers to the maximum deflection achieved by the instrument’s needle when the maximum allowable current (the deflection current) passes through the device. This concept is essential in instrument calibration and design, as it determines the relationship between the measured parameter and the instrument’s reading.

Galvanometer

A galvanometer is an instrument designed to detect and measure small electric currents. It operates on the principle that a current passing through it generates a magnetic field that causes a needle to deflect. Its sensitivity and inherent resistance are critical properties when adapting it for other measurements, such as in a voltmeter.

Transcript

00:01 Okay, so we want to decide a multi -range voltimeter capable of full -scale deflection and we want to be assured to make sure we measure 20 volts, 50 volts and 100 volts.

00:21 Okay, and we know that the resistance of the gapometer is 60 on and it has a full -scale deflection of 1 mili -amp.

00:30 Okay, so i draw here a circuit that is going to help us through this.

00:37 Okay, it has obviously the gavenometer and then it has three resistors in series.

00:44 Okay, remember that when we have resistors in series, the potential difference or voltage divides between them.

00:55 Okay, so i will have three cases.

00:58 Okay, i have.

01:00 Here a selector this red thing is a movable thing that i'm going to change depending of what voltage i want to measure okay so i'm going to the same obviously for the biggest voltage i want i want all of these resistors to carry it so when i have 100 volt i'm using all of the voltage so let's call this three okay when i want to measure 50 volts i have the two first that and i'm going to call two that it's connected obviously through here and when i want to measure the small voltage i mean 20 volts i'm going to measure one okay and this is sorry, this is 20 volts.

01:51 Okay, so depending on which a voltage you have.

01:54 I choose one of the positions and i measure the potential differences.

01:59 Okay? here obviously this is the voltage voltage or the potential difference to be measured okay and then how do i do this i already know that when it's connected to one okay i'm going to see that the total potential difference must be 20 okay i know the current of the gamma parameter so so with this i'm going to give, this is going to give me three different equations.

02:38 Okay, i have three different unknowns.

02:41 When i solve them, i get the values of the resistors.

02:44 Okay, so for the first one, i know that 20 volts, remember this is what i want to measure, must be equal, of, and this is important for you to see when this is connected in one, current flows through here, through here, and comes to this point and comes down here.

03:04 Why is that? because even though, obviously, the circuit, okay, ends in this point, in the 20, in the first point, point to number one.

03:17 Okay.

03:17 So it's not going to go anywhere but there.

03:21 And you see that r2 and r3 does not contribute anything to this.

03:25 So i will have remember om slow.

03:30 And so i have the 20 volt must be equal to the current, that is 1 times 10 to the minus 3 ampere, times the value of the resistor that is r1 plus 60 om.

03:44 Remember, it's a serious configuration, so i have to take into account also the galvanometer resistance...

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