1. An electric current is called alternating current when it
ⓐ. flows only in one direction with constant magnitude
ⓑ. changes only its magnitude but never reverses direction
ⓒ. exists only in a circuit containing a capacitor
ⓓ. changes magnitude and direction periodically
Correct Answer: changes magnitude and direction periodically
Explanation: Alternating current, written as \(\text{AC}\), is not defined merely by a changing value. Its direction also reverses after regular intervals, so the current has positive and negative parts in one complete cycle. A current that only varies in size but does not reverse direction is not the usual sinusoidal \(\text{AC}\) considered in alternating-current analysis. A steady one-direction current is closer to \(\text{DC}\), not \(\text{AC}\). The word alternating points to repeated reversal, not just a random fluctuation in current.
2. A cell connected to a lamp gives a current in one fixed direction, while a mains supply drives current that reverses direction repeatedly. The mains supply is best described as
ⓐ. \(\text{DC}\), because its voltage can have a fixed rating
ⓑ. \(\text{AC}\), because the current direction reverses periodically
ⓒ. \(\text{DC}\), because it can operate a lamp
ⓓ. \(\text{AC}\), because every household device must contain a capacitor
Correct Answer: \(\text{AC}\), because the current direction reverses periodically
Explanation: The basic contrast between \(\text{AC}\) and \(\text{DC}\) is the direction of current. In \(\text{DC}\), the current has one direction in the external circuit, even if its value is not always perfectly constant in every practical case. In \(\text{AC}\), the direction reverses periodically, so the current alternates between opposite directions. Operating a lamp does not by itself decide whether a supply is \(\text{AC}\) or \(\text{DC}\). The deciding feature here is the repeated reversal of current direction.
3. In the beginning of \(\text{AC}\) circuit analysis, a sinusoidal variation is preferred because it represents
ⓐ. a current that increases forever with time
ⓑ. a voltage that must remain positive at all instants
ⓒ. a smooth repeating sinusoidal change
ⓓ. a random change with no fixed repetition
Correct Answer: a smooth repeating sinusoidal change
Explanation: A sinusoidal alternating quantity changes smoothly with time and repeats the same pattern after every cycle. It naturally contains a positive half and a negative half, so it can represent reversal of direction or polarity. It is not a continuously increasing quantity, because its value returns through zero and changes sign. It is also not random, since its pattern has a definite cycle. This regular wave shape is why sinusoidal \(\text{AC}\) becomes the standard starting point for phasors, phase, and circuit calculations later.
4. Use the graph description below.
A graph of current against time is a smooth wave. It rises to a positive maximum, returns to zero, reaches an equal negative maximum, and then returns to zero again in a repeating pattern.
This graph most directly represents
ⓐ. sinusoidal \(\text{AC}\)
ⓑ. steady \(\text{DC}\)
ⓒ. a current with no direction reversal
ⓓ. zero current at all instants
Correct Answer: sinusoidal \(\text{AC}\)
Explanation: The described graph has both positive and negative parts, so the current reverses direction. The repeated smooth pattern shows periodic behaviour, which is a key feature of sinusoidal \(\text{AC}\). A steady \(\text{DC}\) graph would not cross into negative current if the chosen direction is fixed. A current that is zero at all instants would lie along the time axis, not reach positive and negative maxima. The sign change on the graph is the visual clue for alternating direction.
5. The symbol \(i\) in an \(\text{AC}\) circuit usually represents
ⓐ. the maximum value of current in the cycle
ⓑ. current at a particular instant
ⓒ. the heating-equivalent value of current only
ⓓ. the frequency of the alternating current
Correct Answer: current at a particular instant
Explanation: The small symbol \(i\) is commonly used for instantaneous current in an \(\text{AC}\) circuit. Its value depends on the particular instant, so it can change from positive to negative during a cycle. The maximum value is represented separately by \(I_0\), not by \(i\). The heating-equivalent value is represented by \(I_{\text{rms}}\), which has a different physical meaning. Confusing \(i\) with \(I_0\) hides the time-dependent nature of alternating current.
6. Which pair matches the usual \(\text{AC}\) symbol with its meaning?
ⓐ. \(I_0\) — instantaneous voltage
ⓑ. \(v\) — peak current
ⓒ. \(V_0\) — peak voltage
ⓓ. \(f\) — phase angle
Correct Answer: \(V_0\) — peak voltage
Explanation: In standard \(\text{AC}\) notation, \(V_0\) denotes the peak or maximum value of alternating voltage. The instantaneous voltage is written as \(v\), while instantaneous current is written as \(i\). The peak current is represented by \(I_0\), not by \(v\). Frequency is represented by \(f\), while phase angle is commonly represented by \(\phi\). The subscript \(0\) often signals the maximum value in sinusoidal \(\text{AC}\) notation.
7. A data sheet lists a current as \(I_0=5\,\text{A}\). The statement means that
ⓐ. the current is \(5\,\text{A}\) at every instant
ⓑ. the time period is \(5\,\text{s}\)
ⓒ. the phase angle is \(5\,\text{rad}\)
ⓓ. the peak current is \(5\,\text{A}\)
Correct Answer: the peak current is \(5\,\text{A}\)
Explanation: The symbol \(I_0\) denotes the maximum or peak value of current in a sinusoidal \(\text{AC}\). It does not mean that the current remains \(5\,\text{A}\) throughout the cycle. The instantaneous current \(i\) may be smaller than \(5\,\text{A}\), zero, or negative at different instants depending on the phase of the wave. Time period and phase angle use different symbols and units, so they cannot be inferred from \(I_0\) alone. A peak value gives the amplitude scale of the current wave.
8. In \(\text{AC}\) notation, \(V_{\text{rms}}\) is different from \(V_0\) because \(V_{\text{rms}}\) refers to
ⓐ. the maximum possible voltage in a cycle
ⓑ. the instantaneous voltage only at \(t=0\)
ⓒ. the number of voltage cycles completed per second
ⓓ. the heating-equivalent voltage
Correct Answer: the heating-equivalent voltage
Explanation: The symbol \(V_{\text{rms}}\) stands for root mean square voltage, often called the effective value of an alternating voltage. It is not the same as the peak voltage \(V_0\), which is the largest magnitude reached in the cycle. The \(rms\) value is important because many practical ratings are expressed in terms of heating effect. Frequency tells how many cycles occur per second and is written as \(f\), not \(V_{\text{rms}}\). Peak and effective values describe different aspects of the same alternating voltage.
9. Study the table and choose the row in which the symbol and unit are paired suitably.
| Row | Quantity | Symbol | Usual unit |
|---|
| P | Frequency | \(f\) | \(\text{Hz}\) |
| Q | Time period | \(T\) | \(\text{V}\) |
| R | Peak current | \(V_0\) | \(\text{A}\) |
| S | Peak voltage | \(I_0\) | \(\text{V}\) |
ⓐ. Row Q
ⓑ. Row P
ⓒ. Row R
ⓓ. Row S
Correct Answer: Row P
Explanation: Frequency is represented by \(f\), and its unit is \(\text{Hz}\). Time period is represented by \(T\), but its unit is \(\text{s}\), not \(\text{V}\). Peak current is represented by \(I_0\), while peak voltage is represented by \(V_0\). The unit \(\text{A}\) belongs to current and the unit \(\text{V}\) belongs to voltage. The row with \(f\) and \(\text{Hz}\) is the only fully suitable pairing in the table.
10. The time period \(T\) of an alternating quantity describes
ⓐ. the maximum value reached by current
ⓑ. the angle between voltage and current phasors only
ⓒ. the time taken to complete one full cycle
ⓓ. the heating-equivalent value of voltage
Correct Answer: the time taken to complete one full cycle
Explanation: The time period \(T\) tells how long one complete repetition of an alternating waveform takes. It is measured in seconds, written as \(\text{s}\). It is not an amplitude, so it does not describe the largest value of current or voltage. The angle between two alternating quantities is described by phase difference, often represented by \(\phi\). Separating time scale from amplitude scale is essential when reading an \(\text{AC}\) graph.
11. The unit \( \text{rad s}^{-1} \) is most naturally associated with
ⓐ. peak voltage \(V_0\)
ⓑ. rms current \(I_{\text{rms}}\)
ⓒ. time period \(T\)
ⓓ. angular frequency \(\omega\)
Correct Answer: angular frequency \(\omega\)
Explanation: Angular frequency is represented by \(\omega\) and is measured in \(\text{rad s}^{-1}\). It describes how quickly the phase angle of a sinusoidal quantity changes with time. Peak voltage \(V_0\) is measured in \(\text{V}\), while rms current \(I_{\text{rms}}\) is measured in \(\text{A}\). Time period \(T\) is measured in \(\text{s}\), not in angular units per second. The unit \(\text{rad s}^{-1}\) belongs to rate of angular change, not to amplitude.
12. A record of an alternating voltage gives \(v=12\,\text{V}\) at one instant and \(V_0=20\,\text{V}\). The best interpretation is that
ⓐ. \(12\,\text{V}\) is the peak voltage and \(20\,\text{V}\) is the instantaneous voltage
ⓑ. \(v\) and \(V_0\) must always be equal in an \(\text{AC}\) circuit
ⓒ. \(v\) is the instantaneous voltage and \(V_0\) is the peak voltage
ⓓ. \(20\,\text{V}\) is the frequency of the supply
Correct Answer: \(v\) is the instantaneous voltage and \(V_0\) is the peak voltage
Explanation: The small symbol \(v\) represents the instantaneous value of alternating voltage. The symbol \(V_0\) represents the maximum or peak value of that voltage. At a particular instant, \(v\) can be smaller than \(V_0\), equal to zero, or even negative depending on the phase of the cycle. A value written in \(\text{V}\) is a voltage value, not a frequency. The distinction between \(v\) and \(V_0\) prevents treating a changing quantity as if it were fixed at its maximum.
13. A quantity in an \(\text{AC}\) graph is marked by the vertical distance from the central zero line to the highest point of the wave. This marked quantity is
ⓐ. the peak value \(V_0\)
ⓑ. the time period \(T\)
ⓒ. the frequency \(f\)
ⓓ. the phase angle \(\phi\)
Correct Answer: the peak value \(V_0\)
Explanation: The vertical distance from the central zero line to the top of a sinusoidal wave gives the amplitude or peak value. For current, this is written as \(I_0\); for voltage, it is written as \(V_0\). Time period \(T\) is read horizontally as the time for one full cycle, not vertically. Frequency \(f\) is related to how often cycles repeat, while phase angle \(\phi\) describes angular position or separation. A graph of \(\text{AC}\) contains both vertical amplitude information and horizontal time information, so the two should not be mixed.
14. In the phrase \(I_{\text{rms}}\), the subscript \(rms\) is used to show that the value is
ⓐ. always equal to the peak current \(I_0\)
ⓑ. the number of cycles completed in \(1\,\text{s}\)
ⓒ. an effective current value
ⓓ. the phase difference between current and voltage
Correct Answer: an effective current value
Explanation: The notation \(I_{\text{rms}}\) refers to the root mean square current, which is an effective current value. It is different from the instantaneous current \(i\), whose value changes from moment to moment in an alternating cycle. It is also different from \(I_0\), the peak current. Frequency \(f\) counts cycles per second, while phase difference is represented by an angle such as \(\phi\). The subscript in \(I_{\text{rms}}\) signals the type of current value being reported.
15. The phase angle \(\phi\) in elementary \(\text{AC}\) notation is used to describe
ⓐ. phase difference
ⓑ. the unit of current
ⓒ. the maximum value of voltage
ⓓ. the resistance of a wire
Correct Answer: phase difference
Explanation: The symbol \(\phi\) is commonly used for phase angle in \(\text{AC}\) analysis. It helps describe how one sinusoidal quantity is shifted relative to another, such as voltage relative to current. It is not a unit of current, since current is measured in \(\text{A}\). It is also not the peak voltage, which is written as \(V_0\). Phase notation becomes especially useful when comparing waveforms that do not reach their maxima at the same instant.
16. A label on an \(\text{AC}\) source gives \(V_{\text{rms}}=230\,\text{V}\) and \(f=50\,\text{Hz}\). From these labels alone, the two reported quantities are
ⓐ. peak voltage and angular frequency
ⓑ. instantaneous voltage and time period
ⓒ. phase angle and peak current
ⓓ. effective voltage and frequency
Correct Answer: effective voltage and frequency
Explanation: The symbol \(V_{\text{rms}}\) represents the effective or root mean square value of voltage. The symbol \(f\) represents frequency, whose unit is \(\text{Hz}\). The label does not directly state the peak voltage \(V_0\), instantaneous voltage \(v\), or time period \(T\). It also does not give a phase angle \(\phi\) or a peak current \(I_0\). Reading subscripts and units together is the safest way to identify what an \(\text{AC}\) label is reporting.
17. Match the \(\text{AC}\) quantities with their usual units.
| Column I | Column II |
|---|
| P. \(I_{\text{rms}}\) | 1. \(\text{rad s}^{-1}\) |
| Q. \(V_0\) | 2. \(\text{A}\) |
| R. \(T\) | 3. \(\text{s}\) |
| S. \(\omega\) | 4. \(\text{V}\) |
ⓐ. P-4, Q-2, R-1, S-3
ⓑ. P-2, Q-4, R-3, S-1
ⓒ. P-2, Q-3, R-4, S-1
ⓓ. P-1, Q-4, R-3, S-2
Correct Answer: P-2, Q-4, R-3, S-1
Explanation: The root mean square current \(I_{\text{rms}}\) is a current, so its unit is \(\text{A}\). The peak voltage \(V_0\) is a voltage, so its unit is \(\text{V}\). The time period \(T\) is the time for one complete cycle and is measured in \(\text{s}\). Angular frequency \(\omega\) tells the rate of change of phase angle and is measured in \(\text{rad s}^{-1}\). Units help separate amplitude quantities from time and angular-rate quantities.
18. A sinusoidal current has peak value \(I_0\), instantaneous value \(i\), and rms value \(I_{\text{rms}}\). At different instants in a cycle, \(i\) may be
ⓐ. only equal to \(I_0\)
ⓑ. positive, zero, or negative
ⓒ. only equal to \(I_{\text{rms}}\)
ⓓ. always numerically larger than \(I_0\)
Correct Answer: positive, zero, or negative
Explanation: The instantaneous current \(i\) is the value of current at a particular instant. In a sinusoidal alternating current, the current passes through positive values, becomes zero, and then takes negative values during the other half cycle. The peak value \(I_0\) is only the maximum magnitude, not the value at every instant. The rms value \(I_{\text{rms}}\) is an effective value related to heating effect, not the continuously changing instantaneous value. The sign of \(i\) shows direction relative to the chosen positive direction.
19. The notation \(v\) is used instead of \(V_0\) in an \(\text{AC}\) equation when the voltage value is meant to be
ⓐ. instantaneous voltage
ⓑ. the maximum voltage only
ⓒ. the time period of the supply
ⓓ. the number of cycles per second
Correct Answer: instantaneous voltage
Explanation: In \(\text{AC}\) notation, lowercase \(v\) represents instantaneous voltage. It changes with time as the alternating source goes through different parts of its cycle. The symbol \(V_0\) represents the peak voltage, which is the largest magnitude reached by the voltage. Time period \(T\) and frequency \(f\) describe the time behaviour of the waveform, not its instantaneous voltage value. The lowercase symbol reminds us that the value is changing from instant to instant.
20. A source is described by the values \(I_0\), \(V_0\), \(f\), and \(\phi\). The pair that contains one amplitude quantity and one phase-related quantity is
ⓐ. \(V_0,\ \phi\)
ⓑ. \(I_0\) and \(V_0\)
ⓒ. \(f\) and \(V_0\)
ⓓ. \(f\) and \(I_0\)
Correct Answer: \(V_0,\ \phi\)
Explanation: The quantity \(V_0\) is the peak or amplitude value of voltage. The quantity \(\phi\) represents a phase angle or phase difference. The pair \(I_0\) and \(V_0\) contains two amplitude quantities, one for current and one for voltage. Frequency \(f\) gives cycles per second and does not itself represent a phase angle. Separating amplitude from phase is needed before phasor diagrams and lead-lag language can be used correctly.
