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The resonant frequency ($\omega_0$) of a series LCR circuit is given by:
The formula for resonant frequency is given as '$\omega_0 = 1/\sqrt{LC}$' when $X_L = X_C$ or $\omega L = 1/\omega C$.
If the inductive reactance ($X_L$) is greater than the capacitive reactance ($X_C$) in a series LCR circuit, the circuit is said to be predominantly:
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.'
In a series LCR circuit, at resonance, what is the impedance (Z) of the circuit?
At resonance, $X_L = X_C$, so the impedance formula $Z = \sqrt{R^2 + (X_L - X_C)^2}$ simplifies to $Z = \sqrt{R^2 + 0^2} = R$.
A series LCR circuit is tuned to a specific frequency to receive a particular radio station. This phenomenon is an example of:
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.'
When a series LCR circuit is at resonance, the total source voltage appears across which component?
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.'
If the frequency of the energy source driving a system is near its natural frequency, what happens to the amplitude of oscillation?
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.'
Consider a series LCR circuit with $L = 1.00 \text{ mH}$ and $C = 1.00 \text{ nF}$. What is its resonant angular frequency?
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, $\omega_0 = 1/\sqrt{(1.00 \times 10^{-3}) \times (1.00 \times 10^{-9})} = 1/\sqrt{1.00 \times 10^{-12}} = 1/(1.00 \times 10^{-6}) = 1.00 \times 10^6 \text{ rad/s}$.
In a series LCR circuit, if $R = 100 \Omega$, $L = 1.00 \text{ mH}$, and $C = 1.00 \text{ nF}$, and the applied voltage amplitude $v_m = 100 \text{ V}$, what is the peak current ($i_m$) at resonance?
At resonance, the peak current $i_m = v_m/R$. Given $v_m = 100 \text{ V}$ and $R = 100 \Omega$. So, $i_m = 100 \text{ V} / 100 \Omega = 1 \text{ A}$. The provided text also specifically mentions this for the given values: 'Since $i_m = v_m/R$ at resonance, the current amplitude for case (i) is twice to that for case (ii).'
The phase relationship between the current and voltage in a series LCR circuit at resonance is:
At resonance, $X_L = X_C$, which means $(X_L - X_C) = 0$. From $\tan \phi = (X_L - X_C)/R$, we get $\tan \phi = 0$, so $\phi = 0$. This implies current and voltage are in phase.
Which of the following is the correct SI unit for magnetic flux?
According to the NCERT text, 'The SI unit of magnetic flux is weber (Wb) or tesla meter squared ($T m^2$).'
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.