Answer to Question #212298 in Electrical Engineering for Sidra

Question #212298

Apply series and parallel combinations to reduce RLC circuit

Expert's answer

As is customary, the first order of business is to calculate impedance (Z) values for all components depending on the frequency of the AC power supply.

Because this is a series-parallel combination circuit, we must lower its overall impedance in more than one step. The first step is to put L and C2's impedances together to form a series combination of impedances.

Then, that impedance will be coupled in parallel with the resistor's impedance to produce still another impedance combination. Finally, the total impedance will be calculated by adding that quantity to the impedance of C1.

For our table to follow all of these stages, we will need to add more columns to it to represent each step.

Complex addition for series combinations and the "reciprocal" formula for complex impedances in parallel will be required to calculate these new (combination) impedances. This time, there is no avoiding the reciprocal formula: the needed figures can only be obtained in this manner!

We can now use Ohm's Law (E=IZ) to compute voltage drops across C1 and the series-parallel combination of R/(L—C2) vertically in those table columns.

That final step was simply a precaution. There is a lot of room for mistakes in a problem with as many steps as this one. Occasional cross-checks like that may save a person a lot of time and stress by spotting issues before the final step.

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