Basic Electrical Engineering: AC Circuits
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Questions and Answers

What is the average voltage formula derived from the values given?

  • Vave = 0.637 Vm (correct)
  • Vave = Vm / 2
  • Vave = Vm / Ï€
  • Vave = 0.5 Vm

What does the term Vm represent in the context of the given formulas?

  • Maximum voltage (correct)
  • Minimum voltage
  • Root mean square voltage
  • Average voltage

Which mathematical operation is performed to derive Vave from the maximum voltage Vm?

  • Multiplication by a constant
  • Division by Ï€ (correct)
  • Integration of Sin ωt
  • Subtraction of cos functions

Which of the following expressions reflects the relationship between average voltage and the cos function?

<p>Vave = Vm (cos π - cos 0) (B)</p> Signup and view all the answers

In the context of the formulas, what does the integral from 0 to π Sin ωt dωt refer to?

<p>Area under the voltage curve (D)</p> Signup and view all the answers

What does the term 'RMS value' refer to in electrical circuits?

<p>The equivalent DC current that produces the same heat as AC (D)</p> Signup and view all the answers

How is the power factor defined?

<p>The cosine of the angle between voltage and current (A)</p> Signup and view all the answers

What is the unit of frequency?

<p>Hertz (Hz) (A)</p> Signup and view all the answers

What does the term 'reactive power' represent in a circuit?

<p>The power drawn due to the reactive component of current (C)</p> Signup and view all the answers

The formula for active power is given by which expression?

<p>P = VI cos(φ) (A)</p> Signup and view all the answers

What does the peak factor indicate?

<p>The ratio of maximum value to RMS value of an alternating quantity (B)</p> Signup and view all the answers

The unit for apparent power is expressed as?

<p>Volt-Ampere (VA) (B)</p> Signup and view all the answers

What is the form factor for a sine wave defined as?

<p>1.11 (B)</p> Signup and view all the answers

What does the Q-factor represent in a circuit?

<p>Current magnification (B)</p> Signup and view all the answers

Which relationship is true for the inductive susceptance (BL) in a circuit?

<p>BL is inversely proportional to frequency (B)</p> Signup and view all the answers

At resonance frequency, what happens to the admittance (Y) in a circuit?

<p>Y equals the conductance (G) (A)</p> Signup and view all the answers

What happens to the current (I) at resonance frequency in a circuit?

<p>Current is minimum (C)</p> Signup and view all the answers

How is the power factor (P.F.) characterized at resonance frequency?

<p>P.F. is one (unity) (B)</p> Signup and view all the answers

What is the graphical representation of conductance (G) in relation to frequency?

<p>Straight line parallel to frequency (D)</p> Signup and view all the answers

In the Q-factor formula, what do the variables L and R represent?

<p>Inductance and resistance (B)</p> Signup and view all the answers

Which statement correctly describes capacitive susceptance (BC)?

<p>BC is directly proportional to frequency (B)</p> Signup and view all the answers

In a star connection, how do line current and phase current relate?

<p>Line current and phase current are equal. (B)</p> Signup and view all the answers

What is the relationship between line voltage and phase voltage in a star connection?

<p>Line voltage is equal to phase voltage. (D)</p> Signup and view all the answers

In a delta connection, how is the line voltage defined?

<p>Line voltage is the difference between two phase voltages. (B)</p> Signup and view all the answers

Which of the following correctly states the relationship for line voltage in a delta connection?

<p>VRY = VR(ph) - VY(ph) (B)</p> Signup and view all the answers

What remains the same for both line currents and phase currents in a star-connected circuit?

<p>They are equal in magnitude. (C)</p> Signup and view all the answers

What does the instantaneous power drawn by a circuit depend on?

<p>The product of voltage and current (D)</p> Signup and view all the answers

Which component of instantaneous power remains constant with respect to time?

<p>The constant component (D)</p> Signup and view all the answers

In the average power formula, what does $P_{ave}$ equal to?

<p>$V_m I_m \cos \phi$ (D)</p> Signup and view all the answers

What is the effect of the phase shift $,\phi$ in the power formula?

<p>It affects the average power transmitted (C)</p> Signup and view all the answers

What is the relationship between instantaneous voltage $v$ and current $i$ given in the content?

<p>$v = V_m \sin(\omega t)$ (C)</p> Signup and view all the answers

What type of circuit configuration is described as including a resistor, inductor, and capacitor connected in series?

<p>Series RLC circuit (B)</p> Signup and view all the answers

Which formula appropriately represents the instantaneous power $p_t$ derived in the content?

<p>$p_t = V_m I_m \sin \omega t \sin(\omega t + \phi)$ (D)</p> Signup and view all the answers

Which term is part of the average power formula that accounts for the phase shift?

<p>$\cos(\phi)$ (A)</p> Signup and view all the answers

What is the main characteristic of the second component of instantaneous power as described?

<p>It oscillates and varies with time (B)</p> Signup and view all the answers

How is the total power (P) in a balance 3-phase circuit calculated?

<p>P = 3VphIph (D)</p> Signup and view all the answers

What is the significance of the angle 'θ' in the power equation P = VphIph cos(θ)?

<p>It represents the phase angle between the current and voltage. (B)</p> Signup and view all the answers

In the two-watt meter method for power measurement, what does the sum of the readings represent?

<p>Total power of the system. (A)</p> Signup and view all the answers

Which formula correctly calculates the line voltage (VL) based on phase voltage (Vph)?

<p>VL = Vph + 2Vph cos(60) (A)</p> Signup and view all the answers

What characterizes an inductive load in relation to phasor diagrams?

<p>Voltage leads current. (C)</p> Signup and view all the answers

If the phase voltage (Vph) is 60 volts, what is the line voltage (VL) in a star connection?

<p>180 volts (B)</p> Signup and view all the answers

Which value of cos(θ) is used in the power formula for a purely resistive load?

<p>1 (B)</p> Signup and view all the answers

Flashcards

RMS Value

A way to represent alternating current (AC) voltage, calculated using the square root of the mean of the square of the instantaneous values.

Average Value of AC

The average of the instantaneous values of AC voltage over one cycle.

AC Average value formula

Vave = (2Vm)/pi

AC Average Value

0.637 times the peak voltage (Vp).

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Peak Voltage (Vm)

The maximum value of AC voltage.

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Frequency (f)

The number of cycles an alternating quantity completes per second, measured in Hertz (Hz).

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Time Period (T)

The time taken to complete one cycle of an alternating quantity, measured in seconds.

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Power Factor (pf)

The cosine of the angle (φ) between voltage and current in an AC circuit.

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Active Power (P)

The actual power consumed in a circuit, calculated as VIcosφ, where V and I are RMS voltage and current, and φ is the phase angle.

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Reactive Power (Q)

Power drawn by reactive components in a circuit, calculated as VIsinφ.

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Apparent Power (S)

The total power supplied to a circuit, calculated as VI.

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Peak/Crest Factor

Ratio of peak value to RMS value for an alternating quantity.

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Instantaneous Power (AC circuit)

The power at any given instant in an AC circuit, calculated as the product of instantaneous voltage and current.

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Average Power (AC Circuit)

The average power delivered over a complete cycle in an AC circuit; it's the constant component of power ignoring the time-varying part.

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Power Factor (cos φ)

A measure of how effectively power is transferred in an AC circuit; it's the cosine of the phase difference (φ) between voltage and current.

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Series RLC Circuit

An electric circuit containing a resistor (R), inductor (L), and capacitor (C) connected in series.

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Phasor Diagram

A graphical representation of the phasors of voltage and current in a circuit, showing their magnitudes and phase relationships.

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AC Circuit Voltage

Alternating current circuit voltage; a voltage that changes with time.

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AC Circuit Current

Alternating current circuit current; a current that changes with time.

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Instantaneous Power Formula

P(t) = V(t)I(t)

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Average Power Formula

Pavg = VI cos φ

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Phase Difference (φ)

The difference in degree or radian between voltage and current in AC circuit

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Star Connection

A type of three-phase circuit where the ends of the three phase windings are connected to a common point called the neutral (N) and the other ends are connected to the line terminals (R, Y, and B).

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Line Voltage (VL)

The voltage between any two line terminals in a three-phase circuit. In a star connection, it is the vector difference of two phase voltages.

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Phase Voltage (Vph)

Voltage between one line terminal and the neutral point in a star connected circuit.

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Line Current (IL)

The current flowing through the lines in a three-phase circuit. In a star connection, it is the same as the phase current.

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Phase Current (Iph)

The current flowing through each phase winding in a three-phase circuit. In a star connection, it is the same as the line current.

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Q-Factor (RLC Circuit)

A measure of the 'quality' of a resonant circuit. Higher Q means sharper resonance and less energy loss.

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Q-Factor Formula

Q-factor is calculated by dividing the reactance (either inductive or capacitive) at resonance by the resistance.

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Parallel Resonance

A condition in a parallel RLC circuit where the inductive and capacitive reactances cancel each other out, leading to minimum current and maximum impedance.

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Admittance (Y) in Parallel Resonance

Admittance is minimum at the resonant frequency in a parallel RLC circuit.

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Current (I) in Parallel Resonance

Current is also minimum at the resonant frequency in a parallel RLC circuit.

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Power Factor at Resonance

Power factor is unity (1) at the resonant frequency in a parallel RLC circuit.

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Graphical Representation of Parallel Resonance

Admittance is graphed as a curve, with a minimum at the resonant frequency. Inductive Susceptance is inversely proportional to frequency, and Capacitive Susceptance is directly proportional to frequency.

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Comparison of Series and Parallel Resonance

Series resonance has maximum current and minimum impedance at the resonant frequency, while parallel resonance has minimum current and maximum impedance at the resonant frequency.

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Relationship in Star Connection

In a star connection, the line voltage (VL) is equal to the square root of 3 times the phase voltage (Vph): VL = √3 * Vph.

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Power in Three-Phase System

The total power consumed in a balanced three-phase system is the sum of the power consumed in each phase, calculated as P = 3 * Vph * Iph * cosφ.

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Two-Wattmeter Method

A method to measure the total three-phase power using two wattmeters. The sum of the readings gives the total power.

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Circuit Diagram

A simplified representation of a circuit showing the components and their connections using symbols.

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Inductive Load

A load that primarily consists of inductive components, such as motors, transformers, and coils.

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Study Notes

Basic Electrical Engineering

  • This document is lecture notes for a course on AC Circuits.
  • The notes are based on the AICTE model curriculum 2018.
  • The notes are effective from academic year 2018-19.
  • The material is from Aryabhatta Knowledge University, Patna.
  • The notes were prepared for Government Engineering College, Jamui.

AC Circuits: Single-Phase AC Circuits

  • AC generators use Faraday's electromagnetic induction law

  • When a current-carrying conductor cuts a magnetic field, an electromotive force (emf) is induced in the conductor.

  • A single rectangular loop of wire rotating in a magnetic field creates alternating emf.

  • The emf produced is proportional to the rate of change of magnetic flux.

  • The equation for induced emf (e) is e = NBAωsin(ωt)

  • Where: N = number of turns, B = maximum flux density, A = area of coil, ω = angular velocity, t = time

  • Alternating current varies sinusoidally.

  • The maximum value of current is denoted by Im.

Definitions

  • Waveform: The graph of an alternating quantity against time.
  • Cycle: One complete set of positive, negative, and zero values of an alternating quantity.
  • Instantaneous value: The value of an alternating quantity at a specific instant in time.
  • Amplitude/Peak value: The maximum value attained by an alternating quantity.
  • Average value: The average of all instantaneous values over half a cycle.
  • RMS value: The equivalent DC current that produces the same amount of heat as the alternating current over a given time.

AC Circuits: Additional Information

  • Reactive power: Power drawn by reactive components of a circuit.
  • Apparent power: Product of rms voltage and current.
  • Peak factor: Ratio of peak value to rms value (Kf = 1.11 for sine wave).
  • Form factor: Ratio of rms value to average value (Kf = 1.11 for sine wave).
  • Phase difference: Angular displacement between two zero or maximum values of two alternating quantities of same frequency.

Derivation of average value and RMS value of sinusoidal AC signal

  • Average value (Graphical method and Analytical method)
  • RMS value (Graphical method and Analytical method)

AC Circuits: Purely Resistive Circuit

  • In a purely resistive circuit, the current is in phase with the voltage.
  • The instantaneous power is the product of voltage and current.
  • Average power is the product of rms voltage and current.
  • The average power consumed is a purely resistive circuit is equal to the product of voltage and current in root mean square values (VRMS * IRMS).

AC Circuits: Purely Inductive Circuit

  • In a purely inductive circuit, the current lags behind the voltage by 90 degrees.
  • The instantaneous power is the product of voltage and current.
  • The average power consumed in a purely inductive circuit is zero.

AC Circuits: Purely Capacitive Circuit

  • In a purely capacitive circuit, the current leads the voltage by 90 degrees,
  • The average power consumed in a purely capacitive circuit is zero.

Series Resistance-Inductance (R-L) Circuit

  • In an R-L circuit, the current lags the voltage by an angle φ.
  • The instantaneous power is the product of voltage and current.
  • The average power is proportional to Cos φ.

Series Resistance-Capacitance (R-C) Circuit

  • In an R-C circuit, the current leads the voltage by an angle φ.
  • The instantaneous power is the product of voltage and current.
  • The average power varies depending on the current, and voltage values.

Series Resonance RLC Circuit

  • Resonance occurs when the inductive and capacitive reactances are equal.
  • Current is at its maximum.
  • The impedance is equal to resistance R.
  • Q factor = Voltage magnification

Parallel Resonance RLC Circuit

  • Resonance occurs when the inductive and capacitive reactances are equal.
  • Impedance is at maximum.

Comparison between Single and Three-Phase Circuits

  • Three phase circuit has power delivered through three conductors.
  • Single phase circuit has power delivered through one conductor
  • Three phase power system has higher efficiency and is more economical for large industrial loads, and it is used in heavy duty loads

Generation of Three-Phase EMF

  • Three coils are rotated in a magnetic field
  • The coils are separated by 120 degrees.
  • The induced emf in the coils has a 120-degree phase difference

Important definitions

  • Phase voltage
  • Line voltage

Measurement of power in a balanced 3-phase circuit

  • Two wattmeter method
  • Formula: P = W1 + W2

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