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An RLC circuit has a resistance of 200 Ω and an inductance of 15 mH. Its oscillation frequency is 7000 Hz. At time t = 0, the current is 25 mA, and there is no charge on the capacitor. After five complete cycles, the current is

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temdan2001

Answer: 2.13 × 10^-4 A

Explanation:

Given that the RLC circuit has a resistance R = 200 Ω and an inductance L = 15 mH.

Its oscillation frequency F = 7000 Hz

The initial current I = 25 mA = 25/1000 or 25 × 10^-3 A

Since there is no charge on the capacitor, the current after complete 5 circle will be achieved by using the formula in the attached file.

Please find the attached file for the remaining explanation for the solution.

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Lanuel

The current in the RLC circuit after five (5) complete cycles is equal to [tex]2.15 \times 10^{-4} \; Amperes[/tex]

Given the following data:

  • Resistance = 200 Ω
  • Inductance = 15 mH = 0.015 H
  • Oscillation frequency = 7000 Hz
  • Current = 25 mA = 0.025 A

To determine the current in the RLC circuit after five (5) complete cycles, we would use the following formula:

[tex]I_t = I_o e^{\frac{Rt}{2L} coswt}[/tex]

Note: There is no electrical charge on the capacitor.

After five (5) complete cycles, the formula becomes:

[tex]I_5 = I_o e^{\frac{-R}{2L} \frac{5}{F} }[/tex]

Substituting the given parameters into the formula, we have;

[tex]I_5 = 0.025 e^{\frac{-200}{2\; \times \;0.015} \times \frac{5}{7000} }\\\\I_5 = 0.025 e^{\frac{-200}{0.03} \times \frac{5}{7000} }\\\\I_5 = 0.025 e^{\frac{-1000}{210} }\\\\I_5 = 0.025 e^{-4.7619}\\\\I_5 = 0.025 \times 0.0086\\\\I_5 = 0.00215 \\\\I_5 = 2.15 \times 10^{-3} \; Amps[/tex]

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