Introduction to Alternating Current (AC)
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Questions and Answers

What is the primary reason for the preference of AC voltage over DC voltage?

AC voltages can be easily and efficiently converted from one voltage to another using transformers.

The terms AC voltage and AC current are considered contradictory and redundant.

True (A)

What does AC stand for in electrical terms?

  • Alternative Current
  • Alternating Circuit
  • Alternating Current (correct)
  • Alternating Charge

What is the equation for the AC voltage applied to a resistor?

<p>v = vm sin ωt</p> Signup and view all the answers

Who conceived the idea of the rotating magnetic field?

<p>Nicola Tesla</p> Signup and view all the answers

The potential difference in AC voltage can be expressed as ______.

<p>vm sin ωt</p> Signup and view all the answers

What is the SI unit of magnetic field named after?

<p>Nicola Tesla</p> Signup and view all the answers

According to Kirchhoff's loop rule, what is the equation for the current through a resistor in an AC circuit?

<p>i = (vm/R) sin ωt</p> Signup and view all the answers

How is the total impedance (Z) in an AC circuit calculated when given resistance (R), inductive reactance (XL), and capacitive reactance (XC)?

<p>The total impedance (Z) is calculated using the formula $Z = R^2 + (X_L - X_C)^2$.</p> Signup and view all the answers

What is the significance of a negative phase difference, as indicated by the value of -53.1° in an AC circuit?

<p>A negative phase difference indicates that the current lags behind the voltage in the circuit.</p> Signup and view all the answers

Using the given values, how would you calculate the power (P) dissipated in an AC circuit with a current (I) of 40A and resistance (R) of 3Ω?

<p>Power is calculated using the formula $P = I^2 R$, which results in $P = (40A)^2 imes 3Ω = 4800W$.</p> Signup and view all the answers

What is the formula for calculating capacitive reactance (XC) in an AC circuit, and how is it influenced by frequency (ν)?

<p>Capacitive reactance (X_C) is calculated using the formula $X_C = \frac{1}{2 \pi u C}$, showing its inverse relationship with frequency.</p> Signup and view all the answers

Explain the relationship between the power factor and phase angle in an AC circuit.

<p>The power factor is defined as cos(φ), where φ is the phase angle; hence, a phase angle of -53.1° results in a power factor of 0.6.</p> Signup and view all the answers

What condition must be met for a transformer to be considered 100% efficient?

<p>The power input must equal the power output, meaning there are no energy losses.</p> Signup and view all the answers

How does the number of turns in the secondary coil affect the voltage output?

<p>If the secondary coil has more turns than the primary, the voltage is stepped up.</p> Signup and view all the answers

What happens to the current when the voltage is stepped up in a transformer?

<p>The current decreases in the secondary coil compared to the primary coil.</p> Signup and view all the answers

Identify the relationship between voltage and turns for a step-down transformer.

<p>In a step-down transformer, the voltage is reduced (Vs &lt; Vp) while the current increases (Is &gt; Ip).</p> Signup and view all the answers

What is the significance of equation (7.35) in the context of a transformer?

<p>Equation (7.35) represents the relationship between primary and secondary current and voltage ratios.</p> Signup and view all the answers

What are the ideal conditions assumed for deriving the equations related to transformers?

<p>The assumptions include small primary resistance, equal flux linkage, and small secondary current.</p> Signup and view all the answers

Describe the term 'step-up transformer' based on the number of turns in the coils.

<p>A step-up transformer has more turns in the secondary coil than in the primary, increasing voltage.</p> Signup and view all the answers

How does a transformer's efficiency impact its practical application?

<p>High efficiency (over 95%) allows transformers to be used effectively in power systems with minimal energy loss.</p> Signup and view all the answers

How does the current through an inductor compare to the voltage in an AC circuit?

<p>The current reaches its maximum value one-fourth of a period later than the voltage.</p> Signup and view all the answers

Does an inductor consume power in an AC circuit, and why?

<p>No, an inductor does not consume power, as the average power over a complete cycle is zero.</p> Signup and view all the answers

Calculate the inductive reactance of a pure inductor with 25.0 mH at a frequency of 50 Hz.

<p>The inductive reactance is 7.85 Ω.</p> Signup and view all the answers

What is the rms current in a circuit with a 220 V source connected to a pure inductor with an inductive reactance of 7.85 Ω?

<p>The rms current is 28 A.</p> Signup and view all the answers

What happens to current flow in a capacitor when connected to a DC voltage source?

<p>Current flows briefly to charge the capacitor, then stops as the voltage across it builds up.</p> Signup and view all the answers

In an AC circuit with a capacitor, describe the nature of current flow.

<p>Current continuously flows as the capacitor charges and discharges with the alternating voltage.</p> Signup and view all the answers

Define the relationship between instantaneous power in an inductor and the sine function.

<p>The instantaneous power is represented by $p_L = -\frac{i_m v_m}{2} \sin(2\omega t)$.</p> Signup and view all the answers

How does the average power over one complete cycle in an inductor relate to energy consumption?

<p>The average power is zero, indicating that the inductor does not consume energy over a complete cycle.</p> Signup and view all the answers

Calculate the capacitive reactance of a 15.0 µF capacitor connected to a 220 V, 50 Hz AC source.

<p>212 Ω</p> Signup and view all the answers

What is the rms current flowing through a circuit with a capacitor having a capacitive reactance of 212 Ω and a voltage of 220 V?

<p>1.04 A</p> Signup and view all the answers

Given the peak current is 1.47 A, how does it relate to the rms current?

<p>The peak current is $\sqrt{2}$ times the rms current.</p> Signup and view all the answers

What happens to the capacitive reactance and the current when the frequency of the AC source is doubled?

<p>Capacitive reactance is halved and current is doubled.</p> Signup and view all the answers

How does inserting an iron rod into the inductor affect the glow of the light bulb in the circuit?

<p>The glow of the light bulb decreases.</p> Signup and view all the answers

Explain why the inductive reactance increases when the iron rod is introduced into the inductor.

<p>The iron rod magnetizes, increasing the magnetic field and the inductance.</p> Signup and view all the answers

If the initial capacitive reactance is 212 Ω, how can it affect the brightness of the lamp?

<p>Higher capacitive reactance results in lower current, dimming the lamp.</p> Signup and view all the answers

What is the relationship between the reactance and the current in an AC circuit with reactive components?

<p>Higher reactance leads to lower current flow.</p> Signup and view all the answers

What happens to the current in a circuit when the capacitor is fully charged?

<p>The current falls to zero.</p> Signup and view all the answers

How does a capacitor behave when connected to an AC source?

<p>It limits or regulates the current but does not completely prevent the flow of charge.</p> Signup and view all the answers

What is the relationship between instantaneous voltage (v), charge (q), and capacitance (C) for a capacitor?

<p>The instantaneous voltage is given by the formula $v = \frac{q}{C}$.</p> Signup and view all the answers

Using Kirchhoff’s loop rule, what is the equation relating the voltage across the voltage source and the capacitor?

<p>The equation is $v_m \sin(\omega t) = \frac{q}{C}$.</p> Signup and view all the answers

What formula can be used to derive the current (i) in a capacitor driven by an AC supply?

<p>The current is given by $i = \omega C v_m \cos(\omega t)$.</p> Signup and view all the answers

How is the amplitude of the oscillating current (i_m) expressed in terms of angular frequency (ω), capacitance (C), and peak voltage (v_m)?

<p>It is expressed as $i_m = \omega C v_m$.</p> Signup and view all the answers

What role does the term $\frac{1}{\omega C}$ play when comparing AC circuits to purely resistive circuits?

<p>It plays the role of resistance.</p> Signup and view all the answers

What is the alternative expression for the current i in terms of sine function from the cosine function?

<p>The alternative expression is $i = i_m \sin(\omega t + \frac{\pi}{2})$.</p> Signup and view all the answers

Study Notes

Introduction to Alternating Current (AC)

  • Alternating current (AC) is a type of electrical current that changes direction periodically.
  • AC is used in homes, offices, and to power most electrical devices.
  • AC is preferred over direct current (DC) because it can be transformed easily with transformers.
  • Voltage and current in AC circuits vary sinusoidally with time, characterized by amplitude and angular frequency.
  • Nikola Tesla is credited with pioneering AC technology, including the rotating magnetic field principle and the Tesla coil.

AC Voltage Applied to a Resistor

  • A resistor connected to an AC voltage source experiences a current that varies sinusoidally with time.
  • The AC voltage across the resistor is represented by: v = vm sin ω t
  • vm is the maximum voltage and ω is the angular frequency.
  • Applying Kirchhoff's loop rule to the circuit, we obtain the relationship: vm sin ω t = iR
  • The current through the resistor is given by: i = im sin ω t, where im = vm/R and is the maximum current..

Inductor's Behavior in AC Circuits

  • Inductor does not consume power, it stores and releases energy in its magnetic field
  • Average power supplied to an inductor over a complete cycle is zero
  • Inductive reactance (XL) limits the current in a similar way that resistance does in a DC circuit
  • In an AC circuit, the current flowing through an inductor lags behind the voltage across it by a phase angle of Ï€/2
  • XL is directly proportional to the frequency of the AC source and the inductance of the inductor

### Capacitor's Behavior in AC Circuits

  • Capacitor allows current to flow by alternately charging and discharging as the current flow reverses
  • Capacitor opposes the current flow in AC circuits, but does not completely block it unlike in DC circuits
  • Current in a purely capacitive circuit leads the voltage across it by a phase angle of Ï€/2
  • Capacitive reactance (XC) limits the current flow in a similar way that resistance does in a DC circuit
  • XC is inversely proportional to the frequency of the AC source and the capacitance of the capacitor

### Transformers

  • Transformers are devices that transform AC voltage and current without changing the power
  • Power input to a transformer is equal to the power output, assuming no losses
  • Transformers work on the principle of electromagnetic induction
  • Step-up transformer increases voltage and decreases current when Ns > Np
  • Step-down transformer decreases voltage and increases current when Ns < Np
  • Transformer efficiency is typically high, often exceeding 95%

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Description

This quiz explores the fundamental concepts of Alternating Current (AC) including its characteristics, the mathematical representation of voltage and current in circuits, and the historical contributions of Nikola Tesla. Test your knowledge on AC voltage and its application in resistive circuits.

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