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.