A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V. What is the capacitance?

검증된 단계별 안내

Start by recalling the relationship between the peak current (I₀), the peak voltage (V₀), the angular frequency (ω), and the capacitance (C) for an AC circuit: I₀ = ωC * V₀.

Calculate the angular frequency (ω) using the formula ω = 2πf, where f is the frequency. Here, f = 250 kHz, so substitute this value into the formula.

Rearrange the formula I₀ = ωC * V₀ to solve for the capacitance (C): C = I₀ / (ω * V₀).

Substitute the given values into the formula: I₀ = 330 μA (convert to amperes: 330 × 10⁻⁶ A), V₀ = 2.2 V, and ω (calculated in the previous step).

Simplify the expression to find the capacitance (C). Ensure the units are consistent throughout the calculation.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

주요 개념

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

Capacitance

Capacitance is the ability of a capacitor to store electrical charge per unit voltage. It is measured in farads (F) and is defined by the formula C = Q/V, where C is capacitance, Q is the charge stored, and V is the voltage across the capacitor. In AC circuits, capacitance also affects how the capacitor responds to changing voltages.

Peak Current and Peak Voltage

Peak current refers to the maximum instantaneous current flowing through a circuit, while peak voltage is the maximum voltage across a component. In the context of capacitors, these values are crucial for determining how the capacitor behaves under alternating current (AC) conditions, particularly at a specific frequency, such as 250 kHz in this case.

Reactance

Reactance is the opposition that a capacitor or inductor presents to the flow of alternating current due to its capacitance or inductance. For capacitors, the reactance (Xc) can be calculated using the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance. This relationship is essential for understanding how capacitors influence current and voltage in AC circuits.