Question

Two parallel plate capacitors are identical, except that one of them is empty and the other contains a material with a dielectric constant of 4.2 in the space between the plates. The empty capacitor is connected between the terminals of an ac generator that has a fixed frequency and rms voltage. The generator delivers a current of 0.29 A. What current does the generator deliver after the other capacitor is connected in parallel with the first one?

Answer 1

Answer:

current = 1.51 A

Explanation:

Initially the capacitor without any dielectric is connected across AC source

so the capacitive reactance of that capacitor is given as

$x_c = \frac{1}{\omega c}$

now we have

$i = \frac{V_{rms}}{x_c}$

here we know that

$i = 0.29 A$

now other capacitor with dielectric of 4.2 is connected in parallel with the first capacitor

so here net capacitance is given as

$c_{eq} = 4.2c + c = 5.2c$

now the equivalent capacitive reactance is given as

$x_c' = \frac{1}{\omega(5.2c)}$

$x_c' = \frac{x_c}{5.2}$

so here we have new current in that circuit is given as

$i' = \frac{V_{rms}}{x_c'}$

$i' = 5.2 (i) = 5.2(0.29)$

$i' = 1.51 A$