✓ Board-verified
Physics · 2025 · 3 marks
CBSE 2025 · Region 2 · Set 3 · Q24
(a) ac voltage of frequency ω is applied across a series LCR circuit. Draw the phasor diagram and obtain the impedance of the circuit. (b)…
(a)
ac voltage of frequency $\displaystyle \omega$ is applied across a series LCR circuit. Draw the phasor diagram and obtain the impedance of the circuit.
(b)
Discuss'resonance'in a series LCR circuit and write the expression for resonant frequency.
Marking-scheme solution
(a)
$\displaystyle \vec{V}_{L}+\vec{V}_{R}+\vec{V}_{C}=\vec{V}$
$\displaystyle v_{m}^{2}=v_{R m}^{2}+\left(v_{C m}-v_{L m}\right)^{2}$
$\displaystyle =\left(i_{m} R\right)^{2}+\left(i_{m} X_{C}-i_{m} X_{L}\right)^{2}$
$\displaystyle v_{m}^{2}=i_{m}^{2}\left[R^{2}+\left(X_{C}-X_{L}\right)^{2}\right]$
$\displaystyle i_{m}=\frac{v_{m}}{\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}}$
$\displaystyle \Rightarrow Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}$
(b)
When $\displaystyle X_{L}=X_{C}$, the impedance of the series LCR circuit is minimum and the current flowing through it is maximum.
$\displaystyle \omega_{0}=\frac{1}{\sqrt{L C}}$
All Alternating Current questions2025 question paperNCERT solutions: Alternating CurrentPractice Alternating Current →
More from Alternating Current
- Distinguish between reactance and impedance of an ac circuit. Show that an ideal inductor in an ac circuit does not dissipate any power.2024
- An alternating current is given by I=I_0 cos (100 π) t. The least time the current takes to decrease from its maximum value to zero will be:2025
- A resistor of 30 Ω and a capacitor of 250/(π) μ F are connected in series to a 200 V, 50 Hz ac source. Calculate (i) the current in the circuit, and…2023
- A resistor and an ideal inductor are connected in series to a 100 √2 V, 50 Hz ac source. When a voltmeter is connected across the resistor or the…2024
- A transformer is connected to a 200 V ac source. The transformer supplies 3000 V to a device. If the number of turns in the primary coil is 450, then…2025
- An alternating current I=14 sin (100 π t) A passes through a series combination of a resistor of 30 Ω and an inductor of (2/(5 π)) H. Taking √2=1.4,…2023
- Which of the following statements about a series LCR circuit connected to an ac source is correct?2023
- An inductor, a capacitor and a resistor are connected in series across an ac source of voltage. If the frequency of the source is decreased…2023
CBSE Class 12 Physics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.