Question

The power factor of a good choke coil is (a) Nearly zero (b) Exactly zero (c) Nearly one (d) Exactly one

Short answer

The power factor of a good choke coil is (a) nearly zero, as it has very large inductive reactance (XL) compared to its resistance (R), making the ratio \(PF = \frac{R}{X_L}\) very small or close to zero.

Step-by-step solution

Analyze the given formula

Recall the power factor formula: \(PF = \frac{R}{\sqrt{R^2 + X_L^2}}\) As a good choke coil has very large inductive reactance (XL) compared to its resistance (R), we can deduce that: \(X_L >> R\) Now, let's analyze the power factor formula with this condition.

Apply the condition and evaluate the formula

Since \(X_L >> R\), we can consider \(R^2 + X_L^2 \approx X_L^2\). So, the power factor formula becomes: \(PF = \frac{R}{\sqrt{X_L^2}}\) We notice that the denominator now becomes an absolute inductive reactance value, which is significantly larger than resistance.

Compare the numerator and denominator

Now, we can simplify the formula: \(PF = \frac{R}{X_L}\) Given that the inductive reactance of a good choke coil (XL) is very large compared to its resistance (R), we can deduce that the ratio of R to XL will be very small or close to zero.

Choose the correct option

Since the power factor is very small or close to zero, the correct answer is (a) nearly zero.

Key concepts

Inductive Reactance

Inductive reactance is a property of an electrical circuit that opposes changes in the current flowing through it. It happens in circuits with inductors, like choke coils. The symbol for inductive reactance is \(X_L\) and it is measured in ohms. The reactance depends on two main factors: the frequency of the current and the inductance of the coil.

The formula to calculate inductive reactance is:

• \(X_L = 2\pi f L\)

Where \(f\) is the frequency in hertz and \(L\) is the inductance in henrys. This shows that as the frequency or inductance increases, the inductive reactance becomes larger.

In simple terms, the higher the inductive reactance, the more it will hinder any change in the electric current, which is why choke coils can limit or "choke" AC signals. This is an important aspect when considering the power factor of a device or circuit.

Resistance

Resistance is the electrical property that limits the flow of electric current in a circuit. It is represented by the symbol \(R\) and is measured in ohms. Materials with high resistance require more energy to allow current to flow through them, which can cause them to heat up.

The power factor in an electrical circuit is a ratio involving resistance. It's expressed in the formula:

• \(PF = \frac{R}{\sqrt{R^2 + X_L^2}}\)

Here, the resistance is compared to the total impedance, which includes both resistance and reactance. With a good choke coil, because its inductive reactance \(X_L\) is significantly larger than the resistance \(R\), the power factor tends to be very low, or nearly zero.

Understanding resistance helps in designing circuits that efficiently manage energy flow, especially in AC systems where inductive elements like choke coils are present.

Choke Coil

A choke coil is a type of inductor used in electrical circuits to block or "choke" changes in current. It is particularly useful in AC circuits because it allows DC (direct current) to pass through while impeding AC (alternating current).

Choke coils are characterized by high inductive reactance (\(X_L\)), which means they have minimal resistance. This property makes them effective in filtering applications, like tuning radio frequencies or suppressing electromagnetic interference.

The reason the power factor for a good choke coil is nearly zero is due to its high inductive reactance compared to its resistance. Hence, when you calculate its power factor, it results in a very small value, indicating that most of the power is reactive, not real or useful power. This characteristic is crucial in minimizing losses in power transmission and improving energy efficiency in electrical networks.

Electrical Circuits

Electrical circuits are networks that provide a path for electrical current to flow. These circuits consist of various electrical components such as resistors, capacitors, and inductors.

Understanding electrical circuits involves comprehending how voltage, current, and resistance interact according to Ohm's Law, which is expressed as:

• \(V = IR\)

Where \(V\) is voltage in volts, \(I\) is current in amperes, and \(R\) is resistance in ohms.

In AC circuits, additional elements like inductive reactance and capacitive reactance come into play. These elements affect how different frequencies of alternating current are handled by the circuit.

A choke coil, for example, changes how circuits respond to AC signals. This is crucial for applications where you want to avoid interference or signal loss. Understanding the role of each component in an electrical circuit helps in designing systems that are both functional and efficient.