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) $V_a>V_b$

(c) $V_a=V_b$

(b) $i_a>i_b$

(d) $V_a<V_b$

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Answer:

Correct Answer: 17. (a)

Solution:

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

$Z_c=\sqrt{R^{2}+(\frac{1}{C \omega})^{2}}$

Current $i=\frac{V}{Z_c}=\frac{V}{\sqrt{R^{2}+(\frac{1}{C \omega})^{2}}}$

$V_c=iX=\frac{V}{\sqrt{R^{2}+(\frac{1}{C \omega})^{2}}} \times \frac{1}{C \omega}$

$V_c=\frac{V}{\sqrt{(RC \omega)^{2}+1}}$

If we fill a di-electric material like mica instead of air then capacitance $C \uparrow \Rightarrow V_c \downarrow$

So, $V_a>V_b$