Ch 32: AC Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 32: AC Circuits

문제 7b

32장, 문제 7b

A 0.30 μF capacitor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current to and from the capacitor if the emf frequency is 100 kHz?

검증된 단계별 안내

Step 1: Recall the formula for capacitive reactance, which is the opposition to current flow in a capacitor in an AC circuit. The formula is:

X c_{c} = \frac{1}{π}

, where

f

is the frequency of the AC source and

C

is the capacitance.

Step 2: Substitute the given values into the formula for capacitive reactance. Here,

f

= 100 kHz =

100000

Hz and

C

= 0.30 μF =

0.30 \times 10^{-6}

Step 3: Use Ohm's law for AC circuits to find the peak current. The formula is:

I peak = \frac{V}{peak}

, where

V peak

is the peak voltage and

X c

is the capacitive reactance.

Step 4: Substitute the given peak voltage,

V peak = 10

V, and the calculated value of

X c

from Step 2 into the formula for peak current.

Step 5: Simplify the expression to find the peak current, ensuring that all units are consistent. The result will give the peak current to and from the capacitor in amperes.

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주요 개념

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

Capacitance

Capacitance is the ability of a capacitor to store charge per unit voltage, measured in farads (F). In this case, the capacitor has a capacitance of 0.30 μF, which indicates how much electric charge it can hold at a given voltage. The relationship between charge (Q), voltage (V), and capacitance (C) is given by the formula Q = C * V.

AC Voltage and Current

In an alternating current (AC) circuit, the voltage and current vary sinusoidally with time. The peak voltage (V_peak) is the maximum voltage reached, which in this scenario is 10 V. The peak current can be calculated using the capacitive reactance, which depends on the frequency of the AC signal and the capacitance of the capacitor.

Capacitive Reactance

Capacitive reactance (X_C) is the opposition that a capacitor offers to the flow of AC current, calculated using the formula X_C = 1 / (2πfC), where f is the frequency and C is the capacitance. At a frequency of 100 kHz and a capacitance of 0.30 μF, this reactance determines how much current can flow through the capacitor when subjected to the peak voltage.