✓ Board-verified
Physics · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 1 · Q28
(a) 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,…
A resistor of $\displaystyle 30 \Omega$ and a capacitor of $\displaystyle \frac{250}{\pi} \mu \mathrm{~F}$ are connected in series to a $\displaystyle 200 \mathrm{~V}, 50 \mathrm{~Hz}$ ac source. Calculate (i) the current in the circuit, and (ii) voltage drops across the resistor and the capacitor. (iii) Is the algebraic sum of these voltages more than the source voltage? If yes, solve the paradox.
A series LCR circuit with R $\displaystyle =20 \Omega, \mathrm{~L}=2 \mathrm{H}$ and $\displaystyle \mathrm{C}=50 \mu \mathrm{~F}$ is connected to a $\displaystyle 200$ volts ac source of variable frequency. What is
(i)
the amplitude of the current, and (ii) the average power transferred to the circuit in one complete cycle, at resonance ?
(iii)
Calculate the potential drop across the capacitor.
Marking-scheme solution
(a) \[\begin{aligned}
& \because X_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}} \\
& \omega=2 \pi v=100 \pi \\
& X_{\mathrm{C}}=\frac{1}{100 \pi \times 250 / \pi \times 10^{-6}} \\
& \quad=40 \Omega
\end{aligned}
\]
Impedance of the circuit
\[\begin{aligned}
Z & =\sqrt{X_{\mathrm{C}}^{2}+\mathrm{R}^{2}} \\
& =\sqrt{(40)^{2}+(30)^{2}}=50 \Omega
\end{aligned}
\]
(i) Current in the circuit
\[I_{r m s}=\frac{\mathrm{V}_{r m s}}{Z}=\frac{200}{50}=4 \mathrm{~A}
\]
(ii) Voltage drops across the Capacitor,
\[\mathrm{V}_{\mathrm{C}}=I_{r m s} X_{\mathrm{C}}=4 \times 40=160 \mathrm{~V}
\]
Voltage drops across the Resistor,
\[\mathrm{V}_{\mathrm{R}}=I_{\text {rms }} \times \mathrm{R}=4 \times 30=120 \mathrm{~V}
\]
(iii)
The algebraic sum of the two voltages \(\displaystyle \mathrm{V}_{\mathrm{R}}\) and \(\displaystyle \mathrm{V}_{\mathrm{C}}\) is $\displaystyle 280$ V , which
All Alternating Current questions2023 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 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
- The ratio of the number of turns of the primary to the secondary coils in an ideal transformer is 20: 1. If 240 V ac is applied from a source to the…2025
CBSE Class 12 Physics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.