A series R-C circuit is connected to an alternating voltage source. Consider two situations: [NEET (Re) 2015] |
1. When capacitor is air filled. |
2. When capacitor is mica filled. |
Current through resistor is i and voltage across capacitor is V then |
A) \[{{V}_{a}}<{{V}_{b}}\]
B) \[{{V}_{a}}>{{V}_{b}}\]
C) \[{{i}_{a}}>{{i}_{b}}\]
D) \[{{V}_{a}}={{V}_{b}}\]
Correct Answer: B
Solution :
Net reactive capacitance, |
\[V={{V}_{0}}\sin \omega t\] |
\[{{X}_{c}}=\frac{1}{2\pi fC}\] |
So, current in circuit, |
\[I=\frac{V}{Z}=\frac{V}{\sqrt{{{R}^{2}}+{{\left( \frac{1}{2\pi fC} \right)}^{2}}}}\] |
\[\Rightarrow \] \[I=\frac{2\pi fC}{\sqrt{4{{\pi }^{2}}{{f}^{2}}{{C}^{2}}{{R}^{2}}+1}}\times V\] |
Voltage drop across capacitor, \[{{V}_{c}}=I\times {{X}_{c}}\] |
\[=\frac{2\pi fC}{\sqrt{4{{\pi }^{2}}{{f}^{2}}{{C}^{2}}{{R}^{2}}+1}}\times \frac{1}{2\pi fC}\] |
i.e. \[{{V}_{c}}=\frac{V}{\sqrt{4{{\pi }^{3}}{{f}^{2}}{{C}^{2}}{{R}^{2}}+1}}\] |
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