1. Tardigrade
  2. Question
  3. Physics
  4. A 300 Ω resistor is connected in series with a parallel-plate capacitor across the terminals of a 50.0 Hz ac generator. When the gap between the plates is empty, its capacitance is 70/22 μ F. The ratio of the rms current in the circuit when the capacitor is empty to that when ruby mica of dielectric constant k = 5.0 is inserted between the plates, is equal to

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Q. A $300 \,\Omega$ resistor is connected in series with a parallel-plate capacitor across the terminals of a $50.0 \,Hz$ ac generator. When the gap between the plates is empty, its capacitance is $70/22 \, \mu F$. The ratio of the rms current in the circuit when the capacitor is empty to that when ruby mica of dielectric constant $k = 5.0$ is inserted between the plates, is equal to

Electromagnetic Induction

Solution:

$i_{rms} = \frac{E_0}{\sqrt{2}Z} $
$\Rightarrow \frac{i_{rms,1}}{i_{rms, 2}} = \frac{Z_2}{Z_1} $
$= \frac{\sqrt{R^{2} + \left(\frac{1}{\omega kC}\right)^{2}}}{\sqrt{R^{2} + \left(\frac{1}{\omega C}\right)^{2}}} $
Solving : $\Rightarrow \frac{i_{rms, 1}}{i_{rms, 2}} = 0.3$