In an L-R-C series circuit, the components have the following values: L = 20.0 mH, C = 140 nF, and R = 350 Ω.The generator has an rms voltage of 120 V and a frequency of 1.25 kHz. Determine (a) the power supplied by the generator and (b) the power dissipated in the resistor.

검증된 단계별 안내

First, calculate the angular frequency (ω) of the circuit using the formula ω = 2πf, where f is the frequency of the generator. Substitute f = 1.25 kHz into the formula to find ω.

Next, determine the inductive reactance (X_L) using the formula X_L = ωL, where L is the inductance. Substitute the values of ω and L = 20.0 mH to find X_L.

Calculate the capacitive reactance (X_C) using the formula X_C = 1/(ωC), where C is the capacitance. Substitute the values of ω and C = 140 nF to find X_C.

Find the total impedance (Z) of the circuit using the formula Z = √(R² + (X_L - X_C)²). Substitute the values of R, X_L, and X_C to find Z.

Finally, calculate the power supplied by the generator using the formula P = (V_rms²)/Z, where V_rms is the rms voltage of the generator. Then, calculate the power dissipated in the resistor using the formula P_R = (V_rms²)/R.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Impedance in L-R-C Circuits

Impedance is the total opposition a circuit offers to the flow of alternating current, combining resistance (R), inductive reactance (XL), and capacitive reactance (XC). In an L-R-C series circuit, impedance (Z) is calculated using Z = √(R² + (XL - XC)²), where XL = 2πfL and XC = 1/(2πfC). Understanding impedance is crucial for determining the current and power in the circuit.

Power in AC Circuits

In AC circuits, power is calculated using the formula P = Vrms * Irms * cos(φ), where φ is the phase angle between voltage and current. The real power dissipated in the resistor is given by P = I²R, where I is the current through the resistor. This concept helps in calculating both the power supplied by the generator and the power dissipated in the resistor.

Resonance in L-R-C Circuits

Resonance occurs in an L-R-C circuit when the inductive reactance equals the capacitive reactance (XL = XC), resulting in maximum current flow. At resonance, the impedance is minimized, and the circuit behaves purely resistive. Understanding resonance is essential for analyzing the circuit's behavior at different frequencies, especially when calculating power.