All questions of Single-Phase AC Circuits for Electrical Engineering (EE) Exam

Calculation of Quality Factor

To calculate the quality factor (Q) of an RLC circuit, we use the formula:

Q = Resonant Frequency / Bandwidth

Given values:
Resonant Frequency (f) = 50 kHz
Bandwidth (Δf) = 1 kHz

Calculation:
Q = 50 kHz / 1 kHz
Q = 50

Therefore, the quality factor of the series RLC circuit is 50.

This value indicates the sharpness of the resonance peak in the circuit. A higher quality factor signifies a more selective circuit with a narrow bandwidth around the resonant frequency.

's law be applied to AC circuits?

Yes, Ohm's law can be applied to AC circuits, but it needs to be modified to account for the varying voltage and current values in an alternating current circuit. In AC circuits, the relationship between voltage, current, and resistance is given by the impedance formula, which includes a complex term incorporating frequency and reactance.

Explanation:
When a switch is closed or opened in a circuit containing a capacitor, the voltage across the capacitor at the instant of switching is determined by the initial conditions of the circuit.

Initial Conditions:
Before the switch is closed or opened, the capacitor is assumed to be fully charged or discharged. This means that the voltage across the capacitor is either the maximum voltage or zero voltage, depending on its initial state.

Switching at t=0:
At the instant of switching (t=0), the behavior of the capacitor depends on its initial conditions.

If the capacitor is fully charged before switching, it will try to maintain the voltage across its terminals. Therefore, the voltage across the capacitor at t=0 will be zero. This is because the capacitor resists sudden changes in voltage and will discharge through the circuit.

If the capacitor is initially discharged (voltage=0), it will try to prevent any change in voltage across its terminals. Therefore, the voltage across the capacitor at t=0 will be the maximum voltage. This is because the capacitor will charge up rapidly to its maximum voltage as the circuit seeks to establish equilibrium.

Answer:
In the given question, the voltage across the capacitor at the time of switching (t=0) is 0V. This implies that the capacitor is either fully charged or discharged before the switch is closed or opened.

You know voltage magnification is equal to Q facor multiplied by voltage across resistance

Introduction:
In an RLC (resistor-inductor-capacitor) circuit, there are three main components: resistance (R), inductance (L), and capacitance (C). These components interact with each other to form the circuit's impedance, which is a complex quantity that includes both magnitude and phase information. In such circuits, the voltage across and the current through the circuit are related by the impedance.

Explanation:
The vector reference in an RLC circuit is always the voltage (option A). This is because the voltage across the components and the current flowing through them are out of phase due to the presence of reactive components (inductors and capacitors). The voltage across the components represents the total energy stored in the circuit, while the current represents the flow of energy.

Impedance and Phasor Diagram:
To understand why voltage is used as the vector reference, we need to consider the concept of impedance and the phasor diagram representation of an RLC circuit.

- Impedance: In an RLC circuit, the impedance (Z) is the total opposition to the flow of alternating current. It is a complex quantity and is given by Z = R + j(Xl - Xc), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. The impedance determines the relationship between the voltage and current in the circuit.

- Phasor Diagram: A phasor diagram is a graphical representation of the voltage and current in an AC circuit. It uses phasors, which are rotating vectors, to represent the magnitude and phase relationship between the voltage and current.

Why voltage is used as the vector reference:
- Voltage represents the total energy stored in the circuit, and it is the quantity that is in phase with the impedance. Therefore, it provides a consistent reference for the phase relationship between the voltage and current.

- The phasor diagram is constructed using the voltage as the reference vector. The current phasor is then drawn relative to the voltage phasor, with the phase difference between them determined by the impedance.

- By using voltage as the vector reference, it becomes easier to analyze and solve RLC circuits, as the phase relationship between the voltage and current can be directly determined from the phasor diagram.

- Resistance (option B) and impedance (option C) are related to the magnitude of the voltage and current, but they do not provide information about the phase relationship between them.

- Current (option D) is not used as the vector reference because it is affected by both the magnitude and phase of the voltage across the components. Using current as the reference would complicate the analysis of the circuit and make it harder to determine the phase relationship.

In conclusion, voltage is always used as the vector reference in an RLC circuit because it represents the total energy stored in the circuit and provides a consistent reference for the phase relationship between the voltage and current.