CBSE 2023 · Region 3 · Set 1 · Q28 · 3 marks
An ac source $\displaystyle \mathrm{v}=\mathrm{v}_{\mathrm{m}} \sin \omega \mathrm{t}$ is connected across an ideal capacitor. Derive the expression for the (i) current flowing in the circuit, and(ii)reactance of the capacitor. Plot a graph of current i versus $\displaystyle \omega \mathrm{t}$.A series combination of an inductor L , a capacitor C and a resistor $\displaystyle R$ is connected across an ac source of voltage in a circuit. Obtain an expression for the average power consumed by the circuit. Find power factor for (i) purely inductive circuit, and (ii) purely resistive circuit.
An ac source $\displaystyle \mathrm{v}=\mathrm{v}_{\mathrm{m}} \sin \omega \mathrm{t}$ is connected across an ideal capacitor. Derive the expression for the (i) current flowing in the circuit, and
(ii)
reactance of the capacitor. Plot a graph of current i versus $\displaystyle \omega \mathrm{t}$.
A series combination of an inductor L , a capacitor C and a resistor $\displaystyle R$ is connected across an ac source of voltage in a circuit. Obtain an expression for the average power consumed by the circuit. Find power factor for (i) purely inductive circuit, and (ii) purely resistive circuit.
Marking-scheme solution
(a)
\(\displaystyle V_{\mathrm{m}} \operatorname{Sin} \omega \mathrm{t}=\frac{q}{C}\)
\[I=\frac{d q}{d \mathrm{t}}=\frac{d}{d \mathrm{t}}\left(C V_{\mathrm{m}} \sin \omega \mathrm{t}\right)
\]
\(\displaystyle I=\omega C V_{\mathrm{m}} c \cos \omega \mathrm{t}\)
Alternatively:-
\[I=\frac{V_{\mathrm{m}}}{1 / \omega C} \cos \omega \mathrm{t}=I_{\mathrm{m}} \sin (\omega \mathrm{t}+\pi / 2)
\]
(ii)
\(\displaystyle I=\frac{V_{\mathrm{m}}}{1 / \omega C} \sin (\omega \mathrm{t}+\pi / 2)=I_{\mathrm{m}} \sin (\omega \mathrm{t}+\pi / 2)\)
Comparing with \(\displaystyle I_{\mathrm{m}}=\frac{V_{\mathrm{m}}}{1 / \omega C}\)
Reactance of the capacitor; \(\displaystyle X_{c}=\frac{1}{\omega C}\)
Alternating CurrentAC Voltage Applied to a CapacitorApplyshort_answermedium
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CBSE Class 12 Physics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.