Final answer:
The total impedance of the series circuit with a 20-ohm resistor and a capacitor of 110.5 microfarads at 60 Hertz is calculated using the formula for impedance in a series RC circuit, which takes into account both the resistive part and the capacitive reactance.
Step-by-step explanation:
To calculate the total impedance of a series circuit containing a 20-ohm resistor and a capacitor with a capacitance of 110.5 microfarads at a frequency of 60 Hertz, we'd need to consider both the resistive (ohmic) impedance and the capacitive reactance.
The resistive part of the impedance (ZR) is simply the resistance value of 20 ohms.
The capacitive reactance (XC) can be calculated using the formula XC = 1 / (2πfC), where 'f' is the frequency and 'C' is the capacitance. Substituting the given values, we get:
XC = 1 / (2π × 60 Hz × 110.5×10⁻⁶ F)
This will give us the value of XC in ohms, which can be used in the formula for total impedance (Z) in a series RC circuit: Z = √(R² + XC²).
By plugging in the values for R and XC, we can calculate the total impedance of the circuit.