Chapter 7: Alternating Current Short Questions | physics Class 12 CBSE

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Chapter 7: Alternating Current Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Define rms current and state its relation to peak current.

The rms (root mean square) current is the square root of the mean of the square of the instantaneous current over one complete cycle.
It is related to peak current by I = im/√2 = 0.707 im.
The rms current is the equivalent dc current that produces the same average Joule heating as the alternating current.

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Medium

Question 2

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Why is the average current over a complete cycle of ac zero, yet Joule heating occurs in a resistor?

The average current is zero because ac current has equal positive and negative half cycles that cancel over one complete cycle.
Joule heating depends on i²R, and i² is always positive regardless of the direction of current flow.
Therefore, even though the average of i is zero, the average of i² is not zero, resulting in continuous heat dissipation.

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Question 3

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What is inductive reactance? How does it depend on frequency?

Inductive reactance (XL) is the opposition offered by a pure inductor to the flow of alternating current, given by XL = ωL.
It is directly proportional to the frequency of the ac source (XL = 2πνL), so higher frequency means greater reactance.
Its SI unit is ohm (Ω), same as resistance, and it limits current in an inductive circuit similar to how resistance limits current in a resistive circuit.

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Question 4

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State the phase relationship between current and voltage in a pure capacitor connected to an ac source.

In a pure capacitor, the current leads the voltage by π/2 (90°) or one-quarter cycle.
If voltage is v = vm sin(ωt), then current is i = im sin(ωt + π/2), showing the current reaches its maximum one-quarter period before the voltage.
This phase lead arises because current is proportional to the rate of change of charge, which in turn equals C times the rate of change of voltage.

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Question 5

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Define capacitive reactance and state how it varies with frequency and capacitance.

Capacitive reactance (XC) is the opposition offered by a capacitor to ac current, given by XC = 1/(ωC) = 1/(2πνC), measured in ohms.
It is inversely proportional to the frequency of the ac source — higher frequency means lower reactance and greater current.
It is also inversely proportional to the capacitance C — a larger capacitor offers less opposition to ac current.

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Question 6

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What is a phasor? How does it help in the analysis of ac circuits?

A phasor is a vector that rotates about the origin with the angular speed ω of the ac source; its magnitude represents the amplitude of the ac quantity.
The vertical component of the phasor at any instant gives the instantaneous value of the sinusoidally varying quantity (voltage or current).
Phasor diagrams allow the phase relationships between voltage and current in different circuit elements to be shown geometrically, simplifying the addition of out-of-phase quantities.

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Question 7

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Why is the average power supplied to a pure inductor over a complete cycle zero?

In a pure inductor, the current lags voltage by π/2, so the instantaneous power p = im vm sin(ωt−π/2)·sin(ωt) = −(im vm/2)sin(2ωt).
The average of sin(2ωt) over a complete cycle is zero, making the average power zero.
Physically, energy is stored in the magnetic field during one half cycle and completely returned to the source in the next half cycle, so no net energy is dissipated.

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Question 8

Quick Recall

Write the expression for impedance of a series LCR circuit and define the terms.

The impedance of a series LCR circuit is Z = √[R² + (XC − XL)²], where R is resistance, XC is capacitive reactance, and XL is inductive reactance.
Impedance is the effective total opposition to ac current in the circuit, playing the same role as resistance in a dc circuit; its unit is ohm (Ω).
The current amplitude in the circuit is given by im = vm/Z, analogous to Ohm's law for dc circuits.

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Question 9

Quick Recall

State the condition for resonance in a series LCR circuit and write the expression for resonant frequency.

Resonance occurs in a series LCR circuit when the capacitive reactance equals the inductive reactance: XC = XL, i.e., 1/(ω₀C) = ω₀L.
The resonant angular frequency is ω₀ = 1/√(LC), and the resonant frequency is ν₀ = 1/(2π√(LC)).
At resonance, impedance is minimum and equals R, so the current amplitude is maximum: im = vm/R.

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Question 10

Quick Recall

Define power factor. What is its value for a purely resistive circuit and a purely inductive circuit?

Power factor is defined as cos φ, where φ is the phase angle between the applied voltage and the current in the ac circuit; it equals R/Z.
For a purely resistive circuit, φ = 0, so power factor = cos 0 = 1, and maximum power (P = IV) is dissipated.
For a purely inductive circuit, φ = π/2, so power factor = cos(π/2) = 0, and no power is dissipated (wattless current flows).

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Question 11

Quick Recall

What is wattless current? In which type of ac circuit does it occur?

Wattless current is the component of current in an ac circuit for which no power is dissipated, because the phase difference between voltage and current is π/2.
It occurs in purely inductive or purely capacitive circuits where cos φ = 0, so despite a current flowing, the average power P = IV cos φ = 0.
In a series LCR circuit, the component of current perpendicular to the applied voltage (Iq) is the wattless component that contributes nothing to real power.

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Question 12

Quick Recall

State the working principle of a transformer and write the voltage ratio equation.

A transformer works on the principle of mutual induction: an alternating current in the primary coil creates a changing magnetic flux that induces an emf in the secondary coil.
The voltage ratio is Vs/Vp = Ns/Np, where Ns and Np are the number of turns in the secondary and primary coils respectively.
For an ideal (100% efficient) transformer, the current ratio is inversely related: Ip/Is = Ns/Np, ensuring conservation of energy (ipvp = isvs).

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Question 13

Quick Recall

Why can't resonance occur in a circuit containing only R and L (RL circuit)?

Resonance requires the voltages across L and C to cancel each other, as they are equal in magnitude and opposite in phase at the resonant frequency.
In a RL circuit, there is no capacitor, so there is no capacitive reactance to cancel the inductive reactance.
Without this voltage cancellation, the impedance can never reduce to just R, and hence maximum current condition (resonance) cannot be achieved.

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Chapter 7: Alternating Current | Short Questions

Define rms current and state its relation to peak current.

Why is the average current over a complete cycle of ac zero, yet Joule heating occurs in a resistor?

What is inductive reactance? How does it depend on frequency?

State the phase relationship between current and voltage in a pure capacitor connected to an ac source.

Define capacitive reactance and state how it varies with frequency and capacitance.

What is a phasor? How does it help in the analysis of ac circuits?

Why is the average power supplied to a pure inductor over a complete cycle zero?

Write the expression for impedance of a series LCR circuit and define the terms.

State the condition for resonance in a series LCR circuit and write the expression for resonant frequency.

Define power factor. What is its value for a purely resistive circuit and a purely inductive circuit?

What is wattless current? In which type of ac circuit does it occur?

State the working principle of a transformer and write the voltage ratio equation.

Why can't resonance occur in a circuit containing only R and L (RL circuit)?

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