How Does Electrical Impedance Affect Electric Circuits?
Impedance is one of the attributes of electronic components that measure resistance or opposition to the alternating current or direct electric current.
Impedance is a vector quantity that consists of two independent one-dimensional phenomena, viz: resistance and reactance.
The symbol for impedance is Z. It is similar to that of the resistance, the formula for the impedance is as follows:
Z = V (in volts) / I (in amperes)
On this page, we will discuss the impedance definition and how is impedance measured.
What is Electrical Impedance?
Impedance reduces the opposition to the steady direct current ‘electric current’ flowing through the circuit.
The magnitude of the impedance is equal to the potential difference applied across the circuit divided by the maximum current flowing through the circuit.
Bow, let’s consider a scenario to understand the ‘Impedance Definition’ most simply:
Electrical Impedance
Let’s suppose that you are in hurry for your tuition classes and your mother asks you to pour two gallons of milk into small cans and deliver these to your neighbours.
Now, using a funnel would take a lot of time and you would get late for your classes. So, this time the potential difference applied by you is more, also, the milk flow too but the resistance offered is high and because of which you got late and got punishment from your teacher.
Another day, you chose a funnel with a big hole and it saved a lot of time. You did your job well and reached tuition class on time.
Here, the small funnel is the resistance, because of which the current flow or the milk flow to milk cans took time. However, a big funnel is an impedance that reduced opposition to the milk flow.
So, the impedance of the milk flow reduces time.
As we discussed the electrical impedance with real-life scenarios, now, let’s understand what is impedance in Physics.
What is Impedance in Physics?
Electrical Impedance (Z) is the total opposition/resistance that a circuit offers to alternating current.
Impedance is measured in ohms and may include resistance (R), inductive reactance (XL), and capacitive reactance (XC); the total impedance is the algebraic sum of the resistance, inductive reactance, and capacitive reactance. Since the inductive reactance and capacitive reactance are 90o out of phase with the resistance and therefore, their maximum values occur at varying times, we can use vector addition to calculate impedance.
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Impedance
The relationship between impedance and its two components, viz: resistance and inductive reactance can be represented using a vector as shown in the image below:
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In the above image, the amplitude of the resistance component is represented by a vector along the x-axis & the amplitude of the inductive reactance is a vector along the y-axis. The amplitude of the impedance is shown by a vector that initiates from zero to a point that represents both the resistance value in the x-direction and the inductive reactance in the y-direction.
The electrical impedance in an electrical circuit with resistance and inductive reactance can be calculated by using the following equation. If capacitive reactance is present in the circuit, its value is added to the inductive reactance term before squaring.
So, the equation for the above statement is given by:
Z = \[\sqrt{Xl^{2}+R^{2}}\]
Impedance & Ohm’s Law
In the above text, Ohm's Law is stated for a purely resistive circuit. When an inductive reactance or capacitive reactance present in the circuit, Ohm's Law can be written to include the total impedance in the circuit. Therefore, Ohm's law takes the following form:
I = V / Z
In the above equation, Ohm's law simply states that the current (I), in amperes, is proportional to the voltage (V), in volts, divided by the impedance (Z), in ohms.
Please note that the values of resistance or the inductive reactance must be changed to vary the impedance in the circuit.
Impedance vs Resistance
Impedance is just like resistance. It is a value that shows the amount of resistance that a component offers to the flow of electrical current. And just like resistance, the unit of impedance is Ohms (Ω).
However, unlike resistance, the impedance varies with the amount of resistance that a component has to a signal varies on the frequency of the signal. This means that the resistance of the component varies directly with the frequency of the signal entering the electronic component.
Resistance is a value and its measure is independent of frequency; also, it doesn't take into account the frequency of the signal passing through it, because frequency doesn't affect the resistance of non-reactive components. However, reactive components change the amount of resistance they offer in a circuit relies on the input signal's frequency. But impedance varies with the frequency of the signal passing via it. So, this was the difference between resistance and impedance.
FAQs on Electrical Impedance: Definition, Formula & Real-Life Uses
1. What is electrical impedance and how does it differ from resistance?
Electrical impedance (Z) is the total opposition that a circuit presents to the flow of an alternating current (AC). It is a comprehensive measure that includes both resistance and reactance. The key difference lies in their scope:
- Resistance (R): This is the opposition to both direct current (DC) and alternating current (AC). It is caused by collisions of electrons within a material and does not cause a phase shift between voltage and current.
- Impedance (Z): This is relevant only for AC circuits. It is a complex quantity that combines resistance and reactance (opposition from capacitors and inductors). Impedance accounts for the phase difference between voltage and current, making it a vector quantity.
2. What is the formula to calculate the impedance for a series RLC circuit?
The formula for calculating the total impedance (Z) in a series circuit containing a resistor (R), an inductor (L), and a capacitor (C) is given by:
Z = √(R² + (XL - XC)²)
Where:
- Z is the total impedance in ohms (Ω).
- R is the resistance in ohms (Ω).
- XL is the inductive reactance (2πfL) in ohms (Ω).
- XC is the capacitive reactance (1 / (2πfC)) in ohms (Ω).
3. How do resistors, inductors, and capacitors each contribute to the total impedance of an AC circuit?
Each component affects the total impedance in a unique way based on the frequency of the alternating current:
- Resistor (R): Its contribution, resistance, is independent of frequency. It opposes the current without causing any phase shift between the voltage across it and the current through it.
- Inductor (L): It contributes inductive reactance (XL), which is directly proportional to the frequency (XL = 2πfL). As frequency increases, its opposition to the current increases.
- Capacitor (C): It contributes capacitive reactance (XC), which is inversely proportional to the frequency (XC = 1/(2πfC)). As frequency increases, its opposition to the current decreases.
The total impedance is the vector sum of resistance and the net reactance (XL - XC).
4. Why does the impedance of a circuit depend on the frequency of the AC source?
Impedance depends on frequency because its reactive components, inductive reactance (XL) and capacitive reactance (XC), are inherently frequency-dependent. An inductor opposes changes in current, so it offers more opposition (higher XL) to a rapidly changing (high-frequency) current. Conversely, a capacitor stores and releases charge, a process that happens more effectively with a rapidly changing current, thus offering less opposition (lower XC) at higher frequencies. Since impedance Z = √(R² + (XL - XC)²), any change in frequency 'f' alters XL and XC, thereby changing the overall impedance of the circuit.
5. What are some real-life applications and uses of electrical impedance?
Electrical impedance is a fundamental concept with many practical applications in electronics and electrical engineering. Key examples include:
- Audio Speaker Crossovers: Crossover networks use inductors and capacitors to create frequency-dependent impedance paths, directing high-frequency signals to the tweeter and low-frequency signals to the woofer.
- Radio Tuning Circuits: In radios, the impedance of an LC circuit is lowest at a specific resonant frequency. By varying the capacitance, you change this resonant frequency to tune into different radio stations.
- Power Transmission: Understanding the impedance of transmission lines is crucial for minimising power loss and ensuring efficient energy transfer over long distances.
- Impedance Matching: Ensuring the output impedance of a source (like an amplifier) matches the input impedance of a load (like a speaker) is essential for maximum power transfer and signal integrity.
6. What is the SI unit of electrical impedance?
The SI unit of electrical impedance is the ohm (Ω). This is the same unit used for measuring both electrical resistance and reactance (inductive and capacitive).
7. What is meant by impedance matching, and why is it important?
Impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source to be equal to each other. This is important for two main reasons:
- Maximum Power Transfer: When the source and load impedances are matched, the maximum possible power is transferred from the source to the load. This is critical in systems like audio amplifiers connected to speakers or radio transmitters connected to antennas.
- Minimising Signal Reflection: In high-frequency applications like data cables or antennas, a mismatch in impedance can cause parts of the signal to be reflected back towards the source, leading to signal loss and distortion.
8. Can the total impedance of a series RLC circuit be lower than its resistance?
No, the total impedance (Z) of a series RLC circuit can never be lower than its resistance (R). According to the formula Z = √(R² + X²), where X is the net reactance (XL - XC), the impedance is the hypotenuse of a right-angled triangle with resistance and reactance as the other two sides. The term X² is always non-negative (zero or positive). Therefore, the value of Z will always be greater than or equal to R. The minimum possible impedance occurs at resonance when XL = XC, making X=0, and in this specific case, Z = R.
