In the context of electrical circuits and AC (alternating current) fundamentals, let's discuss the variation of impedance (Z) and current (i) with frequency.
Impedance (Z):
Impedance is a complex quantity that represents the opposition that an electrical circuit offers to the flow of AC current. It is similar to resistance in a DC circuit but takes into account both resistance and reactance (inductive or capacitive). Impedance is denoted by the symbol Z and is measured in ohms (Ω).
The impedance of a circuit can be calculated using the following formula:
Z = √(R^2 + (XL - XC)^2)
where:
R is the resistance of the circuit in ohms.
XL is the inductive reactance in ohms.
XC is the capacitive reactance in ohms.
Inductive reactance (XL) and capacitive reactance (XC) are frequency-dependent and are given by the following formulas:
XL = 2πfL
XC = 1 / (2πfC)
where:
f is the frequency of the AC signal in hertz (Hz).
L is the inductance of the circuit in henrys (H).
C is the capacitance of the circuit in farads (F).
As the frequency of the AC signal changes, the values of XL and XC also change, leading to variations in the overall impedance Z.
Current (i):
In an AC circuit, the current flowing through the circuit is also frequency-dependent due to changes in impedance. The relationship between current (i), voltage (V), and impedance (Z) is given by Ohm's law for AC circuits:
i = V / Z
Where:
i is the current flowing through the circuit in amperes (A).
V is the voltage across the circuit in volts (V).
Z is the impedance of the circuit in ohms (Ω).
As the frequency of the AC signal changes, the impedance Z changes, and consequently, the current i also changes.
In summary, as the frequency of an AC signal changes, the impedance (Z) of a circuit changes due to the frequency-dependent nature of inductive and capacitive reactances. This, in turn, affects the current (i) flowing through the circuit according to Ohm's law. The behavior of impedance and current with frequency is crucial in the design and analysis of AC circuits and is fundamental to various applications in electrical engineering and electronics.