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:
- (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, $V_a>V_b$
