Which of the following statements are true regarding alternating current?
(A) In an a.c. circuit containing resistance only, a.c. power is expressed in the same form as d.c. power \( (P = I^2R) \), using a special value of current called root mean square (rms) or effective current, which is denoted by \( I_{rms} \)
(B) a phasor is a vector.
(C) resonance phenomenon is exhibited by a circuit even if both L and C are not present in the circuit.
(D) for circuits used for transporting electric power, a low power factor implies less power loss in transmission.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (B) only
(A) In an a.c. circuit containing resistance only, a.c. power is expressed in the same form as d.c. power \( (P = I^2R) \), using a special value of current called root mean square (rms) or effective current, which is denoted by \( I_{rms} \) — Correct. The average power is \( \overline{P} = I_{\mathrm{rms}}^{2} R \), where \( I_{\mathrm{rms}} = I_0/\sqrt{2} \) is the effective current.
(B) a phasor is a vector. — Correct. A phasor is a vector that rotates about the origin with angular speed \( \omega \); its projection on the vertical axis gives the instantaneous value of the voltage or current.
(C) resonance phenomenon is exhibited by a circuit even if both L and C are not present in the circuit. — Incorrect. Resonance needs \( X_L = X_C \), which is possible only when both an inductor and a capacitor are present; an RL or RC circuit shows no resonance.
(D) for circuits used for transporting electric power, a low power factor implies less power loss in transmission. — Incorrect. For a given power \( P = VI\cos\phi \), a low \( \cos\phi \) needs a larger current, so the transmission loss \( I^2R \) is larger, not smaller.
NCERT (2026-27):
AC Voltage Applied to a Resistor – “… To express ac power in the same form as dc power (P = I2R), a special value of current is defined and used. It is called, root mean square (rms) or effective current (Fig. 7.3) and is denoted by Irms or I.”
Summary – “… A phasor is a vector which rotates about the origin with angular speed ω.”
Resonance – “… It is important to note that resonance phenomenon is exhibited by a circuit only if both L and C are present in the circuit.”
Power in AC Circuit: The Power Factor – “… (a) For circuits used for transporting electric power, a low power factor implies large power loss in transmission.”