A current balance refers to an apparatus that helps one to measure the forces exerted by two currents, flowing between two conductors that carry the currents. The set up used to determine these forces contains two parallel horizontal bars connected in series; hence, the current flows in the opposite direction. The resulting force is usually a repulsive one due to the opposite directions of the current.
Current Balance
A current balance refers to an apparatus that helps one to measure the forces exerted by two currents, flowing between two conductors that carry the currents. The set up used to determine these forces contains two parallel horizontal bars connected in series; hence, the current flows in the opposite direction. The resulting force is usually a repulsive one due to the opposite directions of the current. Since every conductor carries some current, a magnetic field develops around the conductor, with the sole purpose of creating the force experienced, which is given by the equation:
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The magnetic field from a wire that is carrying some current depends with the distance from the center of the wire. The amperes law governs the relationship and takes the form:
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The term [Abbildung in dieser Leseprobe nicht enthalten] is a constant that represents the permeability of free space.
From the experiment carried out, it is clear that the magnitude of the force increased as the current and the mass of the conductor increased. The effective length for attaining a current balance wasAbbildung in dieser Leseprobe nicht enthalten, and the distance from the center of the conductor was [Abbildung in dieser Leseprobe nicht enthalten]
Experimental Data
The conduction bars are connected in series; hence, the current flowing between them is equal (Abbildung in dieser Leseprobe nicht enthalten). The telescope was useful in obtaining the measurement of the position of the movable wire viewing through a telescope lever. The measurement on the scale is [Abbildung in dieser Leseprobe nicht enthalten] and the real distance isAbbildung in dieser Leseprobe nicht enthalten, which represents the real surface separation between the wires. The change in the scale reading with respect to when the wires are in contact is[Abbildung in dieser Leseprobe nicht enthalten]. The distance between the movable rod and the fulcrum is [Abbildung in dieser Leseprobe nicht enthalten] and the perpendicular distance between the scale and the fulcrum is[Abbildung in dieser Leseprobe nicht enthalten]. The equation below represents the relationship of this variable.
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The center-to-center distance between the conduction wires, which is the variable of interest is derived as follows:
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For this case, D is the diameter of the connecting rod.
From the setup, mass was measured in Kilograms (Kg) while current was measured in Amperes (A). The force between the conductors was measured in Newton (N).
The following data was obtained from the Experiment
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Table 1: The results obtained from the experiment
The perpendicular distance between the scale and the fulcrum was measured as [Abbildung in dieser Leseprobe nicht enthalten]. The diameter of the connecting rods was determined as [Abbildung in dieser Leseprobe nicht enthalten]. The distance between the movable rod and the fulcrum was measured as [Abbildung in dieser Leseprobe nicht enthalten]
The length [Abbildung in dieser Leseprobe nicht enthalten]. Other measured values include the [Abbildung in dieser Leseprobe nicht enthalten] and [Abbildung in dieser Leseprobe nicht enthalten]
Calculations
Change in X
The change in the scale reading concerning when the wi
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The value of Z
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The center-to-center distance between the conduction wires was:
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Error analysis
For the determination of the lengths, the following is the level of precision
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For the case of [Abbildung in dieser Leseprobe nicht enthalten], they had four decimal places, and hence the allowed value of precision is:
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These errors must have had a significant impact on the value of the calculated Z.
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Therefore, the value of Z may have experienced an error of [Abbildung in dieser Leseprobe nicht enthalten]. In case of percentage errors, the error will be [Abbildung in dieser Leseprobe nicht enthalten]. In this regard, the level of errors is quite small, and its significance on the final results should be quite small.
Theoretical value of permeability
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Discussion
From the data collected, and using the distance between calculations above, the distance between the center of the wires was determined as [Abbildung in dieser Leseprobe nicht enthalten]. The magnetic field from a wire carrying some current relies on the distance from the center of the wires. From the amperes law, the relationship between the two variables is shown below.
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The values of [Abbildung in dieser Leseprobe nicht enthalten], [Abbildung in dieser Leseprobe nicht enthalten], and [Abbildung in dieser Leseprobe nicht enthalten]are constants. Therefore, equation five above can take a linear form
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The constant [Abbildung in dieser Leseprobe nicht enthalten] in equation (6) is the gradient of the slope of the graph. Since the value of [Abbildung in dieser Leseprobe nicht enthalten], [Abbildung in dieser Leseprobe nicht enthalten] are known, it is possible to determine the experimental value of d from the data obtained.
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The value of [Abbildung in dieser Leseprobe nicht enthalten]is the slope of the graph of [Abbildung in dieser Leseprobe nicht enthalten] against the magnetic force [Abbildung in dieser Leseprobe nicht enthalten]. Therefore, the strength of the magnetic force increases as the current increases.
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Graph 1: the graph of force versus Current [Abbildung in dieser Leseprobe nicht enthalten]
The graph shows a linear relationship between the force exerted by the magnetic field and the current flowing through the second rod. The equation of the slope is:
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[...]
- Quote paper
- Amos Wesonga (Author), 2017, Current Balance. An Experimental Analysis, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/429307
