Important Questions Class 12 Physics Chapter 7: Alternating Current

Important Questions Class 12 Physics Chapter 7: Alternating Current

Alternating Current covers voltage and current that change direction with time. The chapter explains rms values, AC through a resistor, an inductor and a capacitor, the LCR series circuit, phasor diagrams, resonance and quality factor, power in AC circuits and the power factor, LC oscillations and the transformer. Numericals on the LCR circuit and the transformer are common in the board paper.

Here are important questions from Alternating Current with complete answers prepared by Extramarks experts. The set covers average power in a resistor, phase relations in RL and RC circuits, impedance of an LCR circuit, resonance, quality factor and the difference between AC and DC. Practise the phasor diagrams too, as they are asked for 3 marks.

Q1.

A student claims that the average power dissipated in the resistor over one complete cycle is zero because the average value of the alternating current over a complete cycle is zero. Analyse the claim and derive the average power dissipated in the resistor. Hence, justify why an alternating current of rms

Answer:

we get

the average power dissipated is not zero.

The average power over one complete cycle is

Since

Thus,

Therefore,

Q2.

rms voltage across the resistor is equal to the rms voltage across the inductor.

Analyse the phase relation between the applied voltage and current, determine the power factor of the circuit, and justify

Answer:

Therefore,

They must be added vectorially.

Thus,

and not

Therefore,

Q3. A series circuit is connected to an AC source of variable frequency. Explain how the current changes as the frequency is increased from a value below resonance to a value above resonance, and state the condition for resonance.

LCR

Answer: For a series (LCR) circuit, the current is

and the current increases. At resonance,

Hence, Z=R and the current becomes maximum.

Q4.

Answer: Given:

The peak voltage is

The power consumed by the resistor is

Therefore, the heat produced in (2) minutes is

Q5. A bulb and a capacitor are connected in series to an A.C. source. Explain, with reason, how the brightness of the bulb is affected when the frequency of the applied A.C. voltage is increased.

Answer:

Z will decrease as ω increase and so the current in the circuit will increase and the bulb will give more intense light.

Q6.

resistance of the circuit (defined as real part of the complex impedance) and Zis the impedance.

Answer: Power in Series LCR Circuit

Q7. Explain the phenomenon of series resonance in LCR circuit. Derive expressions for:

(a) Q-factor of the circuit

(b) Bandwidth

(c) Current at resonance.

Answer:

impedance. (a) Q-factor (Quality factor) represents the sharpness of resonance.

Q-factor indicates energy storage capacity relative to energy dissipation. Higher Q means sharper resonance and better selectivity.

The voltage across L and C at resonance can be Q times the applied voltage, known as voltage magnification.

Q8. Explain the concept of phasor representation of AC quantities. How does a rotating vector help in understanding AC

Answer: A phasor is a rotating vector that represents the amplitude and phase of a sinusoidal quantity. The length of the phasor represents the

projection on the vertical axis gives the instantaneous value of the AC quantity. Phasor representation simplifies AC circuit analysis by converting time-varying sinusoidal functions into static vectors. Addition and subtraction of AC quantities become vector operations, making calculations easier. Phase relationships between different quantities are visually clear in phasor diagrams.

Q9. A 100 Ω resistor is connected to an AC source of 230 V, 50 Hz. Calculate:

(a) Peak current through the resistor.

(b) Power dissipated in the resistor.

(c) Write equations for instantaneous voltage and current.

Answer:

(a) Peak voltage is given by

Peak current is given by

(b) Power dissipated is given by

(c) Angular frequency is given by

Q10. Explain the fundamental difference between direct current (DC) and alternating current (AC). Derive the expression for instantaneous value of AC voltage and explain the significance of peak value, RMS value, and average value.

Answer: Direct current (DC) flows in one direction with constant magnitude, while alternating current (AC) periodically reverses its direction and varies in magnitude sinusoidally with time. The instantaneous value of AC voltage is given by:

represents the effective value of AC voltage that produces the same heating effect as an equivalent DC voltage.

calculations and comparing AC with DC systems.

Q11. Define quality factor of a series LCR circuit. A circuit has L = 2 H, C = 50 μF, and R = 100 Ω. Calculate the quality factor, bandwidth, and the frequencies at half-power points.

Answer: The quality factor (Q-factor) represents the sharpness of resonance and is defined as the ratio of energy stored to energy dissipated per cycle, or mathematically:

Resonant frequency is given by

Quality factor is given by

Bandwidth is given by

Half-power frequencies are given by

Related Study Material on Extramarks

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