Match List - I with List - II.

	LIST - I		LIST - II
(A)	Purely resistive AC circuit	(I)	No power dissipation
(B)	Purely inductive or capacitive AC circuit	(II)	Power is dissipated only in Resistor
(C)	LCR series AC circuit	(III)	Maximum power dissipation
(D)	Power dissipated at resonance in LCR series AC circuit	(IV)	Power is dissipated in L and C

Choose the correct answer from the options given below:

The correct option is (A)-(III), (B)-(I), (C)-(II), (D)-(III).

Let us understand the behavior of different components in an alternating current (AC) circuit and analyze each item step-by-step:

(A) Purely resistive AC circuit:
In a purely resistive AC circuit, the current and voltage are in the same phase, which means the phase difference between them is $$\varphi =0$$ Therefore, the power factor is $$cos\varphi =cos\left(0\right)=1$$ This leads to the maximum possible power dissipation for a given current and voltage in the circuit. Thus, (A) matches with (III) (Maximum power dissipation).

(B) Purely inductive or capacitive AC circuit:
In a purely inductive or purely capacitive circuit, the phase difference between voltage and current is $$\varphi =\frac{\pi }{2}$$ The average power dissipated over a complete cycle is given by $$P=V_{\text{rms}}{I}_{\text{rms}}cos\varphi$$ Since $$cos\left(\frac{\pi }{2}\right)=0$$ the power dissipation is zero. Such a current is also called wattless current. Thus, (B) matches with (I) (No power dissipation).

(C) LCR series AC circuit:
In a series LCR AC circuit, energy is stored and released alternatively by the inductor (L) and the capacitor (C) without any net consumption of power over a complete cycle. Power is only dissipated across the resistor (R) in the form of heat. Thus, (C) matches with (II) (Power is dissipated only in Resistor).

(D) Power dissipated at resonance in LCR series AC circuit:
At resonance in a series LCR circuit, the inductive reactance equals the capacitive reactance, i.e., $$X_L=X_C$$ This makes the total impedance of the circuit purely resistive (Z = R). Under this condition, the phase angle becomes $$\varphi =0$$ and the power factor is maximum (equal to 1). Consequently, the circuit behaves like a purely resistive circuit, and the power dissipation is at its maximum. Thus, (D) matches with (III) (Maximum power dissipation).

Combining all the matches, we get:
(A) - (III), (B) - (I), (C) - (II), (D) - (III)