Answer :
The current amplitude (Imax) in the AC-LRC circuit with the given component values is approximately 0.793 A, considering a 926 Hz voltage source with an rms voltage of 28.5 V.
To find the current amplitude (Imax) in the AC-LRC circuit, we'll follow:
1. Calculate the angular frequency (ω) using the formula:
[tex]\[\omega = 2\pi f\] where f is the frequency of the source (926 Hz). \[\omega = 2\pi \times 926 \approx 5809.48 \text{ rad/s}\][/tex]
where f is the frequency of the source (926 Hz).
[tex]\[\omega = 2\pi \times 926 \approx 5809.48 \text{ rad/s}\][/tex]
2. Calculate the impedance (Z) of the circuit using the formula:
[tex]\[Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}\][/tex]
where:
- R is the resistance of the circuit (35.9 Ω).
- ω is the angular frequency calculated above.
- L is the inductance of the circuit (3.99 mH or 3.99 × 10⁻³ H).
- C is the capacitance of the circuit (385 μF or 385 × 10⁻⁶ F).
[tex]\[Z = \sqrt{(35.9)^2 + (5809.48 \times 3.99 \times 10^{-3} - \frac{1}{5809.48 \times 385 \times 10^{-6}})^2}\][/tex]
[tex]\[Z \approx 35.900 \, \Omega\][/tex]
3. Calculate the current amplitude (Imax) using the formula:
[tex]\[I_{\text{max}} = \frac{V_{\text{rms}}}{Z}\][/tex]
where Vrms is the rms voltage of the source (28.5 V).
[tex]\[I_{\text{max}} = \frac{28.5}{35.900} \approx 0.793 \, \text{A}\][/tex]
So, the current amplitude (Imax) in the AC-LRC circuit is approximately 0.793 A.
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