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

current = 1.51 A

Step-by-step explanation:

Initially the capacitor without any dielectric is connected across AC source

so the capacitive reactance of that capacitor is given as

`x_c = (1)/(\omega c)`

now we have

`i = (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' = (1)/(\omega(5.2c))`

`x_c' = (x_c)/(5.2)`

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

`i' = (V_(rms))/(x_c')`

`i' = 5.2 (i) = 5.2(0.29)`

`i' = 1.51 A`