Chapter 21, Problem 23Q

(a)

To determine

To Discuss: The way frequency of the source emf affects the impedance of pure resistance.

Answer to Problem 23Q

Impedance of a pure resistance will be unaffected by making any changes in the frequency of source EMF.

Explanation of Solution

Introduction: Impedance is the effective opposition (or resistance) against AC. Any signal source has an associated source impedance. Opposition to the flow of electron is known as resistance. It is measured in ohms.

Frequency of the source EMF doesn’t affect the impedance of any pure resistance. The

impedance of pure resistance is independent of change in frequency. Basically, the circuit containing only a pure resistance of R ohms in the alternative current circuit is termed as pure resistive alternative current circuit. 

(b)

To determine

To Discuss: The way frequency of the source emf affects impedance of pure capacitance.

Answer to Problem 23Q

Impedance of a pure capacitance is $X_C=\frac{1}{2\pi fC}$

Explanation of Solution

Introduction: Impedance is the effective opposition (or resistance) against AC. Any signal source has an associated source impedance. Capacitance of the capacitor is a measure of the ability to store charges of capacitor.

The impedance of pure capacitance changes inversely with the frequency of the source EMF according to the $X_C=\frac{1}{2\pi fC}$ . When the source frequency gets so small, impedance of the capacitance turns large. When the source frequency gets so large, impedance of capacitor turns small.

(c)

To determine

To Discuss: The way frequency of the source emf affects impedance of pure inductance.

Answer to Problem 23Q

Impedance of a pure inductance is $X_L=\frac{1}{2\pi fL}$ .

Explanation of Solution

Introduction: Impedance is the effective opposition (or resistance) against AC. Any signal source has an associated source impedance. The flux leakage in the line per unit current flowing is known as inductance.

The impedance of pure inductance changes directly with the frequency of source $\text{EMF }$ according to the $X_L=\frac{1}{2\pi fL}$ .

When the source frequency gets so small, impedance of inductor gets small. When the source frequency gets so large, impedance of inductance gets also large.

(d)

To determine

To Discuss: The way frequency of source emf affects impedance of $LRC$ circuit near resonance.

Answer to Problem 23Q

The impedance rises rapidly when the source frequency will be either decreased or increased a small amount from resonance frequency.

Explanation of Solution

Introduction: Impedance is the effective opposition (or resistance) against AC. Any signal source has an associated source impedance. An electrical circuit which includes series combination or parallel combination of any resistor, an inductor, a capacitor is defined as $LRC$ circuit.

An impedance of $LRC$ circuit with small resistance R, near resonance is extremely sensitive to the frequency of source EMF. If in any condition, the frequency is set at resonance precisely, where $X_L=X_C$ , impedance of the $LRC$ circuit will be very small and also, equal to R.

(e)

To determine

To Discuss: The way frequency of source emf affects impedance of $LRC$ circuit far from resonance.

Answer to Problem 23Q

When the source frequency is lower than resonance, an impedance will be inversely proportional to the frequency of a source emf.

Explanation of Solution

Introduction: Impedance is the effective opposition (or resistance) against AC. Any signal source has associated source impedance. An electrical circuit which includes series combination or parallel combination of any resistor, an inductor, a capacitor is defined as $LRC$ circuit.

The impedance of $LRC$ circuit with small resistance R, far from resonance depends on two things, whether the source frequency is higher or lower than resonance, and then impedance is directly proportional to the frequency of source EMF. So,

• At very high frequency, impedance of circuit is equals to $2\pi fL$ .
• At very low frequency, impedance of circuit is equals to $\frac{1}{2\pi fC}$ .