NEET Alternating Current MCQs & PYQs

Peak voltage across resistor is \(V_R = I_0 R\). Peak source voltage is \(V_0 = I_0 Z\). Since \(Z \ge R\), \(V_R \le V_0\). So A is false. Peak voltage across inductor is \(V_L = I_0 X_L\). At resonance, if \(X_L > R\), then \(V_L\) can be greater than \(V_0\) (voltage magnification). So R is true. Thus, A is false and R is true.

Power rating of \(AC\) devices always refers to average power. However, \(AC\) voltage or current values (e.g., 220V) are typically Root Mean Square (RMS) values, not average values. For a full cycle, the average value of sinusoidal \(AC\) is zero.

Average power consumed by passive circuits is non-negative. Instantaneous power \(p = vi\) can be negative during parts of an \(AC\) cycle, especially in reactive circuits, when energy is temporarily returned to the source.

Metal detectors use \(LC\) resonant circuits. When a metal object enters the coil's magnetic field, it changes the coil's inductance, altering the circuit's resonant frequency and triggering detection.

Smaller bandwidth implies a higher quality factor \(Q\) and sharper resonance, leading to better frequency selectivity (easier tuning). Resonant frequency \(\omega_0\) is the *geometric mean* \(sqrt{\omega_1 \omega_2}\,\) not the arithmetic mean of half-power frequencies.

At resonance, the inductive reactance \(X_L\) equals the capacitive reactance \(X_C\), making the total impedance purely resistive \(Z=R\). This results in the current and emf being in phase. Since impedance is minimal \(Z=R\), the current is maximal. Therefore, R is the correct explanation of A.

For frequencies greater than resonant frequency, inductive reactance \(X_L = \omega L\) becomes greater than capacitive reactance \(X_C = 1/(\omega C)\), making the circuit inductive. The reciprocal of reactance is defined as susceptance. Both statements are true, but R does not explain A.

When resistance \(R\) in a series \(LCR\) circuit decreases, the peak current \(I_{max} = V/R\) at resonance increases, making the peak taller. The quality factor \(Q = (\omega_0 L)/R\) increases, leading to a narrower resonance curve. The resonant frequency \(omega_0 = 1/\sqrt{LC}\) remains unchanged, but the overall resonance behavior (sharpness, peak current) is affected. Therefore, (A) is true and (R) is false.

The impedance of a series \(LCR\) circuit is given by \(Z = \sqrt{R^2 + (X_L - X_C)^2}\). Since \((X_L - X_C)^2\) is always non-negative, \(Z\) is always greater than or equal to \(R\). Thus, (A) is false. The minimum impedance occurs at resonance, where \(Z_{min} = R\). This minimum value depends only on \(R\) and not on the angular frequency \(omega\). Thus, (R) is also false.

A choke coil is an inductor with high inductance and low resistance, used to limit AC current without much power loss. A capacitor also provides reactance \(X_C = 1/(\omega C)\) in an AC circuit, limiting AC current without dissipating significant power. Thus, a capacitor of suitable capacitance can indeed replace a choke coil for AC current limiting applications, so (A) is true. Reason (R) states that a capacitor blocks DC and allows AC, which is a fundamental property of a capacitor. This property (allowing AC) is why it can function as a reactive element in AC circuits, including current limiting, similar to a choke coil. Therefore, (R) is the correct explanation for (A).