SATHEE: Alternating Current - Result Question 17

Alternating Current - Result Question 17

17. A series R-C circuit is connected to an alternating voltage source. Consider two situations:

[2015 RS]

(A) When capacitor is air filled.

(B) When capacitor is mica filled.

Current through resistor is $i$ and voltage across capacitor is $V$ then :

(a) $V_{a} > V_{b}$

(b) $i_{a} > i_{b}$

(d) $V_{a} < V_{b}$

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Answer:

Correct Answer: 17. (a)

Solution:

(a) For series $R - C$ circuit, capacitive reactance,

$Z_{c} = \sqrt{R^{2} + (\frac{1}{C ω})^{2}}$

Current $i = \frac{V}{Z_{c}} = \frac{V}{\sqrt{R^{2} + (\frac{1}{C ω})^{2}}}$

$V_{c} = i X = \frac{V}{\sqrt{R^{2} + (\frac{1}{C ω})^{2}}} \times \frac{1}{C ω}$

$V_{c} = \frac{V}{\sqrt{(R C ω)^{2} + 1}}$

If we fill a di-electric material like mica instead of air then capacitance $C ↑\Rightarrow V_{c} ↓$

So, $V_{a} > V_{b}$

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Alternating Current - Result Question 17

17. A series R-C circuit is connected to an alternating voltage source. Consider two situations:

Answer:

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