CBSE Class 12 Physics (2026–27)
Chapter 7: Alternating Current (AC)
20 Important Questions and Answers
These questions are based on the latest CBSE syllabus and focus on important topics such as RMS value, reactance, LCR circuits, resonance, power factor, and transformers.
Q1. What is an alternating current? How does it differ from direct current?
Answer:
Alternating Current (AC) is an electric current whose magnitude and direction change periodically with time. It is generally represented as (I = I_0 \sin \omega t). In AC, electrons oscillate back and forth instead of moving in one fixed direction. Direct Current (DC), on the other hand, flows only in one direction and maintains nearly constant magnitude. AC is preferred for long-distance transmission because its voltage can be easily stepped up or down using transformers, reducing power losses. Household electricity supply is AC, while batteries provide DC. The frequency of AC in India is 50 Hz, meaning the current completes 50 cycles every second.
Q2. Define RMS value of alternating current.
Answer:
The Root Mean Square (RMS) value of an alternating current is the value of direct current that produces the same heating effect in a resistor as the AC does over one complete cycle. It is also known as the effective value of AC. For a sinusoidal current,
[I_{rms}=\frac{I_0}{\sqrt{2}}]
where (I_0) is the peak current. Similarly,
[V_{rms}=\frac{V_0}{\sqrt{2}}]
for voltage. The RMS value is important because voltmeters and ammeters calibrated for AC measure RMS values. Thus, a 220 V AC supply means 220 V RMS and not the peak voltage.
Q3. What is inductive reactance? Write its expression.
Answer:
Inductive reactance is the opposition offered by an inductor to the flow of alternating current. It arises because a changing current produces a changing magnetic field, which induces a back emf according to Lenz’s law. The inductive reactance is represented by (X_L) and is given by:
[X_L=\omega L=2\pi fL]
where (L) is inductance and (f) is frequency of AC. Its unit is ohm (Ω). Inductive reactance increases with increase in frequency. Therefore, an inductor allows low-frequency currents more easily than high-frequency currents. In a purely inductive AC circuit, current lags the voltage by 90°.
Q4. Define capacitive reactance and write its formula.
Answer:
Capacitive reactance is the opposition offered by a capacitor to the flow of alternating current. It arises because the capacitor continuously charges and discharges during each cycle of AC. The capacitive reactance is represented by (X_C) and is given by:
[X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}]
where (C) is capacitance and (f) is frequency. Its unit is ohm (Ω). Unlike inductive reactance, capacitive reactance decreases with increase in frequency. Thus, capacitors allow high-frequency currents to pass more easily. In a purely capacitive circuit, current leads the voltage by 90°.
Q5. Explain phase difference in a purely resistive AC circuit.
Answer:
When an alternating voltage is applied across a pure resistor, Ohm’s law is valid at every instant. The current through the resistor changes exactly in the same manner as the applied voltage. Therefore, both current and voltage reach their maximum, minimum, and zero values simultaneously. This means there is no phase difference between them.
[\phi = 0^\circ]
As a result, current and voltage are said to be in phase. The average power consumed in a resistor is maximum because the power factor (\cos \phi) is equal to 1. All the electrical energy supplied is converted into heat energy in the resistor.
Q6. Why does current lag voltage in a pure inductor?
Answer:
When AC flows through an inductor, the changing current produces a changing magnetic field. This changing magnetic field induces a self-induced emf that opposes the change in current according to Lenz’s law. Due to this opposition, the current takes time to build up and hence lags behind the applied voltage.
The phase difference between voltage and current is:
[\phi = 90^\circ]
Thus, current lags voltage by one-quarter cycle. Since the average power consumed over a complete cycle is zero, a pure inductor does not dissipate electrical energy as heat. Instead, it stores energy temporarily in its magnetic field and returns it to the source.
Q7. Why does current lead voltage in a capacitor?
Answer:
In a capacitor, current is required to charge and discharge the plates. As soon as an alternating voltage is applied, charging begins immediately. Therefore, the current reaches its maximum value before the voltage attains its maximum value. This causes current to lead voltage.
The phase difference is:
[\phi = 90^\circ]
Hence, current leads voltage by one-quarter cycle. A pure capacitor does not consume average power because the energy stored in the electric field during one part of the cycle is returned to the source during another part. Therefore, the average power consumed is zero.
Q8. What is impedance in an AC circuit?
Answer:
Impedance is the total opposition offered by an AC circuit to the flow of alternating current. It is represented by (Z) and includes both resistance and reactance. For a series LCR circuit:
[Z=\sqrt{R^2+(X_L-X_C)^2}]
Its unit is ohm (Ω). Impedance plays the same role in AC circuits as resistance does in DC circuits. The current in an AC circuit is given by:
[I=\frac{V}{Z}]
A larger impedance results in a smaller current. The concept of impedance is essential in analyzing AC circuits and determining phase relationships.
Q9. What is a series LCR circuit?
Answer:
A series LCR circuit consists of an inductor (L), capacitor (C), and resistor (R) connected in series with an AC source. The same current flows through all three components. The resistor dissipates energy, while the inductor and capacitor store energy in magnetic and electric fields respectively.
The impedance of the circuit is:
[Z=\sqrt{R^2+(X_L-X_C)^2}]
Depending on the values of (X_L) and (X_C), the circuit may behave as inductive, capacitive, or purely resistive. Series LCR circuits are widely used in tuning radio and communication devices because they exhibit resonance.
Q10. What is resonance in a series LCR circuit?
Answer:
Resonance is the condition in a series LCR circuit when inductive reactance equals capacitive reactance.
[X_L=X_C]
At resonance, the impedance becomes minimum and equal to resistance only.
[Z=R]
Therefore, the current in the circuit becomes maximum. The resonant frequency is given by:
[f_r=\frac{1}{2\pi\sqrt{LC}}]
At this frequency, voltage and current are in phase and the power factor becomes unity. Resonance is used in radio receivers, television circuits, and communication systems for selecting desired frequencies.
Q11. Define resonant frequency.
Answer:
The resonant frequency is the frequency at which a series LCR circuit attains resonance. At this frequency, inductive reactance equals capacitive reactance and the net reactance becomes zero.
f_r=\frac{1}{2\pi\sqrt{LC}}
At resonance, impedance becomes minimum and current becomes maximum. The circuit behaves like a pure resistor. Resonant frequency depends only on the values of inductance and capacitance. It plays an important role in tuning circuits used in radio receivers and wireless communication systems.
Q12. What is power factor?
Answer:
Power factor is defined as the cosine of the phase angle between voltage and current in an AC circuit.
[\text{Power Factor}=\cos\phi]
It indicates the fraction of supplied power that is actually utilized. The average power consumed is:
[P=V_{rms}I_{rms}\cos\phi]
A power factor of 1 means maximum efficiency, while a low power factor indicates wastage of electrical energy. In industries, capacitors are often used to improve power factor. Better power factor reduces transmission losses and improves the efficiency of electrical systems.
Q13. What is wattless current?
Answer:
Wattless current is the current that flows in an AC circuit without consuming any average power. It occurs in purely inductive or purely capacitive circuits where the phase difference between current and voltage is 90°.
[P=V_{rms}I_{rms}\cos90^\circ=0]
Although current flows through the circuit, no net electrical energy is converted into heat or work. Energy is merely exchanged between the source and the electric or magnetic field of the capacitor or inductor. Wattless current is undesirable in power transmission because it increases current without contributing useful power.
Q14. State the principle of a transformer.
Answer:
A transformer works on the principle of mutual induction. When alternating current flows through the primary coil, it produces a changing magnetic flux in the iron core. This changing flux links the secondary coil and induces an emf in it according to Faraday’s law of electromagnetic induction.
Transformers are used to increase or decrease AC voltage. They operate only with alternating current because a changing magnetic flux is required for induction. Transformers play a crucial role in power transmission and distribution systems by minimizing energy losses.
Q15. Differentiate between step-up and step-down transformers.
Answer:
A step-up transformer increases voltage and decreases current. In it, the number of turns in the secondary coil is greater than that in the primary coil.
[N_s>N_p]
A step-down transformer decreases voltage and increases current. In it,
[N_s<N_p]
Step-up transformers are used at power stations for transmission, while step-down transformers are used near consumers for domestic supply. Both work on mutual induction and help in efficient electrical power distribution. The voltage ratio is proportional to the turns ratio of the transformer.
Q16. Write two energy losses in a transformer and their reduction methods.
Answer:
Two important energy losses in transformers are:
- Eddy Current Loss: Induced currents in the iron core produce heat. This loss is reduced by laminating the core into thin insulated sheets.
- Hysteresis Loss: Repeated magnetization and demagnetization of the core consume energy. It is minimized by using soft iron or silicon steel cores.
Other losses include copper loss and flux leakage. Reducing these losses improves transformer efficiency, which may exceed 95% in practical transformers. Efficient transformers are essential for economical transmission of electrical energy.
Q17. Why is AC preferred over DC for long-distance transmission?
Answer:
AC is preferred for long-distance transmission because its voltage can be easily increased or decreased using transformers. By stepping up the voltage, the current becomes small for the same power transmission.
Since power loss is:
[P=I^2R]
a smaller current greatly reduces transmission losses. At the receiving end, the voltage is stepped down to safe values for domestic and industrial use. Such easy voltage transformation is not possible with DC using simple transformers. Therefore, AC transmission is more economical and efficient than DC transmission over large distances.
Q18. What are LC oscillations?
Answer:
LC oscillations are electrical oscillations produced in a circuit containing only an inductor and a capacitor. Initially, the capacitor stores electrical energy. When discharged through the inductor, the energy converts into magnetic energy. Later, the magnetic field collapses and charges the capacitor again with opposite polarity.
Thus, energy continuously oscillates between electric and magnetic forms. Ideally, these oscillations continue indefinitely without loss. In practical circuits, resistance causes damping. LC oscillations form the basis of tuned circuits used in radio transmitters, receivers, and many electronic communication systems.
Q19. What is the significance of phase angle in an AC circuit?
Answer:
The phase angle ((\phi)) is the angular difference between voltage and current in an AC circuit. It indicates whether the circuit behaves as resistive, inductive, or capacitive.
- For a resistor: (\phi = 0^\circ)
- For an inductor: (\phi = 90^\circ)
- For a capacitor: (\phi = -90^\circ)
The phase angle determines the power factor ((\cos\phi)) and therefore the average power consumed in the circuit. A smaller phase angle results in a higher power factor and better efficiency. Understanding phase relationships is essential for AC circuit analysis and electrical power management.
Q20. State the transformation ratio of a transformer.
Answer:
The transformation ratio of a transformer is the ratio of secondary voltage to primary voltage. It is equal to the ratio of the number of turns in the secondary coil to those in the primary coil.
[\frac{V_s}{V_p}=\frac{N_s}{N_p}]
If the ratio is greater than 1, the transformer is step-up; if less than 1, it is step-down. In an ideal transformer, power remains constant, so an increase in voltage is accompanied by a decrease in current and vice versa. The transformation ratio helps determine the performance and application of a transformer in electrical systems.