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Determine the series equivalent circuit at f = 1.6 kHz. R₁ = 4.9kQ, R₂ = 1.1kΩ, C = 200nF, L = 120mH

The equivalent circuit is a ....... circuit.

In the equivalent circuit, the resistor is of ........kΩ. help (numbers)
Following this, in addition to the resistor, the remaining element in the equivalent circuit is of .........
Note: If it is a R only circuit, input '0' and 'NA'.

User Strager
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1 Answer

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Final answer:

To find the series equivalent circuit at 1.6 kHz, we calculate the inductive and capacitive reactances and then combine them with the resistances. If the reactances cancel out, the circuit is resistive; otherwise, it includes the predominant reactive component.

Step-by-step explanation:

To determine the series equivalent circuit at f = 1.6 kHz, one must consider the given components: R1 = 4.9kΩ, R2 = 1.1kΩ, C = 200nF (capacitor), and L = 120mH (inductor). To find the equivalent circuit, one must calculate the impedances of the inductor (ZL) and the capacitor (ZC), and then combine them with the resistances.

The inductive reactance (XL) is given by XL = 2πfL, and the capacitive reactance (XC) is given by XC = 1 / (2πfC). At 1.6 kHz, these values are:

  • XL = 2π(1600)(0.12) Ohms
  • XC = 1 / (2π(1600)(200 x 10-9)) Ohms

The ZL and ZC will either add or subtract depending on their magnitudes and the frequency in relation to the circuit's resonant frequency. Since the student is likely seeking a simple answer, it would be necessary to perform these calculations and then sum R1 and R2 for the total resistance in series (Rtotal) of the equivalent circuit.

If ZL and ZC are equal and cancel each other, the circuit is purely resistive (R only). Otherwise, the circuit will have a complex impedance, but for the purposes of schoolwork and likely limitations in complexity, we'd look at the resistive component and the dominating reactive component (inductor or capacitor) to describe the equivalent circuit.

User Iba
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