Alternating Current MCQs for NEET — Physics Questions with Answers

The NCERT text states, 'It is important to note that resonance phenomenon is exhibited by a circuit only if both L and C are present in the circuit. Only then do the voltages across L and C cancel each other (both being out of phase).'

The context mentions, 'At resonant frequency, the current amplitude is maximum; $i_m = v_m/R$.'

The NCERT text clearly states, 'This means that we cannot have resonance in a RL or RC circuit.' This is because for resonance, both L and C must be present.

The formula for resonant frequency is given as '$\omega_0 = 1/\sqrt{LC}$' when $X_L = X_C$ or $\omega L = 1/\omega C$.

The text states, 'If $X_C < X_L$, $\phi$ is negative and the circuit is predominantly inductive. Consequently, the current in the circuit lags the source voltage.'

At resonance, $X_L = X_C$, so the impedance formula $Z = \sqrt{R^2 + (X_L - X_C)^2}$ simplifies to $Z = \sqrt{R^2 + 0^2} = R$.

The NCERT text describes, 'Resonant circuits have a variety of applications, for example, in the tuning mechanism of a radio or a TV set. ... In tuning, we vary the capacitance of a capacitor in the tuning circuit such that the resonant frequency of the circuit becomes nearly equal to the frequency of the radio signal received. When this happens, the amplitude of the current with the frequency of the signal of the particular radio station in the circuit is maximum.'

At resonance, 'the voltages across L and C cancel each other... and the current amplitude is $v_m/R$, the total source voltage appearing across R.'

The text explains resonance as, 'If such a system is driven by an energy source at a frequency that is near the natural frequency, the amplitude of oscillation is found to be large.'

The resonant angular frequency is given by $\omega_0 = 1/\sqrt{LC}$. Given $L = 1.00 \text{ mH} = 1.00 \times 10^{-3} \text{ H}$ and $C = 1.00 \text{ nF} = 1.00 \times 10^{-9} \text{ F}$. So, $\omega_0 = 1/\sqrt{(1.00 \times 10^{-3}) \times (1.00 \times 10^{-9})} = 1/\sqrt{1.00 \times 10^{-12}} = 1/(1.00 \times 10^{-6}) = 1.00 \times 10^6 \text{ rad/s}$.