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Series and Parallel Connections - Lab Report Example

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The purpose of this experiment was to test the theoretical analysis of series-parallel networks through direct measurements; measure properly the voltages and currents of a series-parallel network, and determine the reputation of measured values. This experimentinvolved three…
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Series and Parallel Connections
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Series and Parallel Connections in DC circuits The purpose of this experiment was to test the theoretical analysis of series-parallel networks through direct measurements; measure properly the voltages and currents of a series-parallel network, and determine the reputation of measured values. This experimentinvolved three circuits set ups: one for which resistors are in series, another with resistors connected in parallel. It was realized thatKirchhoff’s Laws for current and voltage are given by equations 1 and 2.
Equation1:
Equation 2:
For circuit devices in series, the voltage drop across the entire series of devices is given by
=
For circuit devices in parallel arrangement, the voltage across each is the same, therefore the junction law applies.
It was also realized that the either total or equivalent resistancecircuits connected in series is found by:
Equivalent resistance for circuits in parallel in found by:
The relationship in the equation below gives a summary of the voltage divider rule as was discovered in the experiment.The voltage is divided based on the resistor values alone. Resistors in a series circuit divides the voltage Vs in the ratio Rx : R eq.Large resistors get large voltage drops.
Equation 3:
In order to check on consistency in measurement, the formula below was used for calculation of error; given that .
Equation 4.
Fig. Plot of uncertainty region for data sheet 1, circuit 1
Red spots: calculated value from measurement; Yellow spots: the values from direct measurement.
Conclusion
Around any closed loop in a circuit, the algebraic sum of potential differences must equal zero. In circuit#1=.Two data points are experimentally consistent if they overlap about a common region of uncertainty. Such data points are convincingly the same.From data sheet 1, circuit1;;;, from direct reading. Applying equation 4 above gives.and.From this,lies between the range 2.67847- 2.50556.Comparing this with the range for the direct reading of, the regions of uncertainty of the two data points overlap as shown by the plot in fig. 1 above. The experimental data are therefore consistent. Read More
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