Question

A 250 - ω resistor is connected in series with a 4.80 - μf capacitor. the voltage across the capacitor is vc=(7.60v)⋅sin[(120rad/s) t ]. part a determine the capacitive reactance of the capacitor.

Answer 1

The capacitive reactance of the capacitor is about 1740 Ω

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Further explanation

Let's recall Capacitive Reactance and Impedance formula as follows:

$\boxed{ X_c = \frac{1}{ \omega C } }$

where:

Xc = capacitive reactance ( Ohm )

ω = angular frequency ( rad/s )

C = capacitance ( F )

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$\boxed{ Z^2 = R^2 + (X_L - X_c)^2}$

where:

Xc = capacitive reactance ( Ohm )

XL = inductive reactance ( Ohm )

R = resistance ( Ohm )

Z = impedance ( Ohm )

Let us now tackle the problem!

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Given:

resistance = R = 250 Ω

capacitance = C = 4.80 μF = 4.80 × 10⁻⁶ F

angular frequency = ω = 120 rad/s

maximum voltage across the capacitor = Vc_max = 7.60 V

Asked:

capacitive reactance of the capacitor = Xc = ?

Solution:

$X_c = \frac{1}{ \omega C }$

$X_c = \frac{1}{ 120 \times 4.80 \times 10^{-6} }$

$\boxed {X_c \approx 1740\ \Omega}$

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Conclusion :

The capacitive reactance of the capacitor is about 1740 Ω

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Learn more

• The three resistors : brainly.com/question/9503202
• A series circuit : brainly.com/question/1518810

• Compare and contrast a series and parallel circuit : brainly.com/question/539204

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Answer details

Grade: High School

Subject: Physics

Chapter: Alternating Current

Answer 2

553 ohms The Capacitive reactance of a capacitor is dependent upon the frequency. The lower the frequency, the higher the reactance, the higher the frequency, the lower the reactance. The equation is Xc = 1/(2*pi*f*C) where Xc = Reactance in ohms pi = 3.1415926535..... f = frequency in hertz. C = capacitance in farads. I'm assuming that the voltage and resistor mentioned in the question are for later parts that are not mentioned in this question. Reason is that they have no effect on the reactance, but would have an effect if a question about current draw is made in a later part. With that said, let's calculate the reactance. The 120 rad/s frequency is better known as 60 Hz. Substitute known values into the formula. Xc = 1/(2*pi* 60 * 0.00000480) Xc = 1/0.001809557 Xc = 552.6213302 Rounding to 3 significant figures gives 553 ohms.