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

  1. When capacitor is air filled.
  2. When capacitor is mica filled.

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

  • Option 1)

    \text{V}_\text{a} > \text{V}_\text{b}

  • Option 2)

    \text{i}_\text{a} > \text{i}_\text{b}

  • Option 3)

    \text{V}_\text{a} = \text{V}_\text{b}

  • Option 4)

    \text{V}_\text{a} < \text{V}_\text{b}

 

Answers (1)
V Vakul

As discussed in

Impedence -

Z= sqrt{X_{C}^{2}+R^{2}}=sqrt{R^{2}+left ( frac{1}{omega c} 
ight )^{2} }

-

 

 

 

Current through resister i= current in the circuit

\frac{V_{o}}{\sqrt{R^{2}+X_{c}^{2}}}=\frac{V_{o}}{\sqrt{R^{2}+\left( \frac{1}{wc} \right )^{2}}}

Voltage acrons capacitor V=\:^{i}X_{c}

\frac{V_{o}}{\sqrt{R^{2}+\left( \frac{1}{wc} \right )^{2}}} \times \frac{1}{wc}= \frac{V_{o}}{\sqrt {R^{2}w^{2}c^{2}+1}}

As,\:\:C_{a}<C_{b}

\therefore i_{a}<i_{b} \:\:\:and\:\:\:V_{a}>V_{b}

 


Option 1)

\text{V}_\text{a} > \text{V}_\text{b}

This option is correct.

Option 2)

\text{i}_\text{a} > \text{i}_\text{b}

This option is incorrect.

Option 3)

\text{V}_\text{a} = \text{V}_\text{b}

This option is incorrect.

Option 4)

\text{V}_\text{a} < \text{V}_\text{b}

This option is incorrect.

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