An inductor is connected to a 15 kHz oscillator. The peak current is 65 mA when the rms voltage is 6.0 V. What is the value of the inductance L?

검증된 단계별 안내

Step 1: Understand the relationship between the inductive reactance (X_L), the frequency (f), and the inductance (L). The formula for inductive reactance is:

X L = 2 π f L

, where X_L is the inductive reactance, f is the frequency, and L is the inductance.

Step 2: Recall the relationship between the rms voltage (V_rms), the peak current (I_peak), and the inductive reactance (X_L). The peak current is related to the rms current (I_rms) by:

I rms = I peak / \sqrt{2}

. Then, the rms voltage and rms current are related by:

V rms = I rms X L

Step 3: Calculate the rms current (I_rms) using the given peak current (I_peak = 65 mA). Use the formula:

I rms = I peak / \sqrt{2}

. Substitute the value of I_peak into the equation.

Step 4: Solve for the inductive reactance (X_L) using the formula:

X L = V rms / I rms

. Substitute the values of V_rms (6.0 V) and I_rms (calculated in Step 3) into the equation.

Step 5: Finally, calculate the inductance (L) using the formula:

L = X L / 2 π f

. Substitute the values of X_L (calculated in Step 4) and f (15 kHz) into the equation to find L.

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주요 개념

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

Inductance

Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. It is measured in henries (H) and is defined as the ratio of the induced electromotive force (emf) to the rate of change of current. Higher inductance values indicate a greater ability to store energy.

RMS Voltage and Peak Current

RMS (Root Mean Square) voltage is a way of expressing the effective value of an alternating current (AC) voltage, which is equivalent to a DC voltage that would deliver the same power. The peak current refers to the maximum instantaneous current flowing through the circuit. In AC circuits, these values are related through the impedance of the circuit, which includes resistance and reactance.

Impedance in AC Circuits

Impedance is the total opposition that a circuit offers to the flow of alternating current and is a combination of resistance and reactance. In inductive circuits, the reactance is frequency-dependent and increases with frequency. The relationship between voltage, current, and impedance is described by Ohm's law, adapted for AC as V = I * Z, where V is voltage, I is current, and Z is impedance.