# Determination of unknown resistance using a DC bridge

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Describe the method of measuring resistance with a voltmeter and ammeter. Under what conditions in each circuit can an unknown resistance be determined using formula (2.1)?

The resistance of any electrical installation or section of the electrical circuit can be determined using an ammeter and voltmeter, using Ohm's law. When turning on the devices according to the scheme, and not only the measured current I passes through the ammeterxbut also current Ivflowing through a voltmeter. Therefore resistance

Where Rv - resistance of the voltmeter.

When turning on the devices according to the scheme, the voltmeter will measure not only the voltage drop Ux at a certain resistance, but also the voltage drop in the winding of the ammeter UA = IRBUT. therefore

Where RBUT - resistance of the ammeter.

In cases where the instrument resistances are unknown and, therefore, cannot be taken into account, it is necessary to use the circuit when measuring low resistances, and when measuring large resistances. In this case, the measurement error determined in the first circuit by current Iv, and in the second - the voltage drop UA, will be small compared to the current Ix and voltage Ux

How is unknown resistance determined by substitution?

This method is based on the fact that if at some section of the circuit the conductor is replaced (replaced) by another of the same resistance, then the current strength in the circuit will not change.

To measure resistance by the substitution method, proceed as follows. Measure current in a circuit with unknown resistance Rxthen replace this resistance with the resistance store R0 and choose the resistance of the store so that the current strength in the circuit becomes the same. The resistance entered in the store will give the value of the measured resistance. The accuracy of the measurement by the substitution method is determined by the accuracy class of the ammeter and resistance store 6.

What is the Wheatstone Bridge?

The Wheatstone Bridge Method is one of the most accurate resistance measurement methods. Measured resistance Rx and three other R, Rb R2 is connected so that a closed quadrangle is formed. Such a system is called the Wheatstone Bridge, a Rx. R, Rb R2 - shoulders of the bridge. Distinguish between balanced and unbalanced bridge. With an arbitrary ratio of the shoulders of the bridge, the bridge is unbalanced (current flows through the galvanometer). There is one definite relationship between the shoulders of a bridge in which the bridge is balanced: 1g=0. Derive the formula for calculating the unknown resistance in the bridge method.

Wheatstone Bridge consists of four resistances - shoulders, which are interconnected so that they form a closed quadrangle. To its two opposite corners BUTand ATconnect the poles of a direct current source E, and to the other two FROMand Dconnect a sensitive galvanometer or potential difference meter. The schematic diagram of the Wheatstone bridge is shown in Fig. 10.

If the bridge is connected to the source E, on the section of the bridge SDdue to the inequality of the potentials of the points FROMand Dan electric current may flow and the galvanometer needle will deflect. In order to SDthere was no current, equality of potentials of points is necessary FROMand D(equilibrium condition for the bridge).

Change the potential difference between points FROMand Dpossible in this way: as a plot ADVcalibrated wire (reochord) with sliding contact is switched on D.Reochord is equipped with a scale. By moving the rechord slider, you can achieve a lack of current in the area SDthat will be registered by a galvanometer. Denote the current strength in the area ADVacross I1, and on the site DIA- across I2. For each of the four arms of the rechord, we write the equations according to Ohm's law:

Where , , , - point potentialsBUT, FROM, AT, Drespectively.

In the absence of current through the galvanometer . Therefore, you can write:

, , (2.05.4)

. (2.05.5)

Thus, the equilibrium condition of the bridge is determined only by the ratio of the rechord shoulders and does not depend on the electromotive force of the source that feeds the circuit.

Since the wire from which the reochord is made ADV,homogeneous and has the same length over the entire length, then the resistanceRHELLandRFar Eastproportional to the corresponding shoulder lengthsl1andl2reohorda. Therefore (2.05.5) can be rewritten as:

, (2.05.6)

whence the unknown resistance:

. (2.05.7)

## Determination of unknown resistance using a DC bridge

Teaching aid for laboratory work No. 3.4 in the discipline "Physics"

Far Eastern Federal University

Determination of unknown resistance using a DC bridge: educational-methodical. manual for laboratory work No. 3.4 in the discipline "Physics" / Far Eastern Federal University, School of Natural Sciences [comp. O. Plotnikova]. - Vladivostok: Dalnevost. federal University, 2013 .-- p.

The manual, prepared at the Department of General Physics of the School of Natural Sciences of the FEFU, contains a brief theoretical material on the topic “Resistance of an electric circuit. Laws of a direct current ”and instruction in laboratory work“ Determination of unknown resistance using a direct current bridge ”in the discipline“ Physics ”.

For bachelor students of FEFU.

Objective: Get familiar with the method of calculating the parameters of an electric circuit based on the use of bridge circuits (DC bridge), find an unknown resistance using a bridge.

## Electrical resistance.

When current flows through a metal conductor, current carriers moving directionally experience collisions with ions located in the nodes of the crystal lattice. This determines the presence of electrical resistance in the conductors. Resistance depends on the material of the conductor, its temperature, and dimensions. For a cylindrical conductor (for example, a wire), the resistance can be found by the formula:

, (1)

where ρ is the resistivity depending on the material of the conductor and its temperature, is the length of the conductor, S is the cross-sectional area of ​​the conductor.

The dependence of resistance on temperature for metal conductors is expressed by the formula:

, (2)

where ρ0- resistivity at 0 0 С, t - conductor temperature, α - temperature coefficient (α = 0,004 K -1).

The unit of resistance in the SI system is Ohm.

## Ohm's laws.

For a homogeneous section of the chain, Ohm's law is expressed by the formula:

, (3)

where U is the voltage in this section, R is the resistance of the section, I is the current strength in it.

For a heterogeneous (containing a current source) section Ohm's law:

, (4)

where r0- internal resistance of the current source, ε- emf source.

For a closed circuit, Ohm's law:

. (5)

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