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A 10-? resistor is connected in series with a 20-?f capacitor. what is the impedance at 1.0 khz?

User Dbuchet
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Answer:

To calculate the impedance of a series circuit consisting of a resistor and a capacitor, we need to consider the individual impedance values of each component at the given frequency. The impedance of a resistor is equal to its resistance (R), while the impedance of a capacitor is given by the formula 1/(2πfC), where f represents the frequency and C is the capacitance.

In this case, we have a 10-ohm resistor and a 20-microfarad (μF) capacitor. To find the impedance at 1.0 kHz (or 1000 Hz), we can use the following formulas:

Impedance of resistor (Zr) = R = 10 ohms

Impedance of capacitor (Zc) = 1/(2πfC) = 1/(2π * 1000 * 20 * 10^(-6)) ohms

Now, let's calculate the impedance of the capacitor:

Zc = 1/(2π * 1000 * 20 * 10^(-6))

= 1/(2π * 20000 * 10^(-6))

= 1/(125.66)

≈ 0.00796 ohms

Since the resistor and capacitor are connected in series, we can find the total impedance (Zt) by summing up the individual impedances:

Zt = Zr + Zc

= 10 + 0.00796

≈ 10.00796 ohms

Therefore, at a frequency of 1.0 kHz, the impedance of the series circuit composed of a 10-ohm resistor and a 20-μF capacitor is approximately 10.00796 ohms.

User Shwetha
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