Final answer:
Measured values of series and parallel resistor combinations are typically compared to calculated values, with series having a total resistance greater than any individual resistor, and parallel having total resistance less than the smallest individual resistor. Measurements consider uncertainties and real-world data is compared against theoretical calculations. The equivalent resistance calculations for both types of connections are checked against the experimental measurements, acknowledging slight deviations due to tolerances and measurement errors.
Step-by-step explanation:
The measured values of the series and parallel resistor combinations are typically compared to calculated values to verify the principles of series and parallel circuits. For resistors in series, the total series resistance should be the sum of the individual resistances and therefore greater than any individual resistance. However, for resistors in parallel, the total parallel resistance should be less than the smallest individual resistor due to the reciprocal relationship in the calculation of equivalent resistance. Upon measuring the voltage across each resistor and the current flowing through the circuit, these theoretical calculations can be checked against the real-world data, keeping in mind that real-world measurements include uncertainties and may differ slightly from ideal calculations due to tolerances and measurement errors.
When assessing the reasonableness of the values, we check if the power is greater for devices in parallel than for those in series, given that power is related to both voltage and current. Analysis of currents involves comparing the currents through individual resistors and considering the sum of currents through parallel branches to ensure they align with the conservation of charge. Voltage measurements across parallel resistors should be the same if they are connected directly across the same potential difference.
To determine if the observations from the experiment are consistent with the theory, one would calculate the equivalent resistance for resistors using the formulated equations for series and parallel combinations and then compare these calculations with the experimental measurements. For example, the total resistance for a parallel combination of resistors is found by applying the formula 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn and entering the known values to determine the equivalent resistance.