Electromagnetic Induction and Alternating Current 6 Question 12
####12. A series $R-C$ circuit is connected to AC voltage source. Consider two cases; $(A)$ when $C$ is without a dielectric medium and $(B)$ when $C$ is filled with dielectric of constant 4. The current $I_{R}$ through the resistor and voltage $V_{C}$ across the capacitor are compared in the two cases. Which of the following is/are true?
(a) $I_{R}^{A}>I_{R}^{B}$
(b) $I_{R}^{A}<I_{R}^{B}$
(c) $V_{C}^{A}>V_{C}^{B}$
(d) $V_{C}^{A}<V_{C}^{B}$
(2011)
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Answer:
Correct Answer: 12. (b, c)
Solution:
- $Z=\sqrt{R^{2}+X_{C}^{2}}=\sqrt{R^{2}+\frac{1}{\omega C}^{2}}$
In case (b), capacitance $C$ will be more. Therefore, impedence $Z$ will be less. Hence, current will be more.
Further, $\quad V_{C}=\sqrt{V^{2}-V_{R}^{2}}=\sqrt{V^{2}-(I R)^{2}}$
In case (b), since current $I$ is more.
Therefore, $V_{C}$ will be less.
