Question

The rms voltage across a 2.50 uF capacitance is 25.0 V if the rms currents for the frequencies 100 Hz, 1000 Hz and 5000 Hz are I₁, I₂ and I₃ respectively, then one can say

I₁ > I₂ >I₃

I₁ > I₃ >I₂

I₃ > I₂ >I₁

I₃ > I₁ >I₂

Answer 1

The capacitive reactance of the capacitor is

X_C =1 / 2$\pi$fC

Here, frequency is f and capacitance is C.

Now, the rms current flows through the capacitor is

I_rms = V_rms/ X_C

         = V_rms / (1 / 2$\pi$fC)

      = V_rms 2 $\pi$fC

For I₁,

I1 = (25.0 V) 2 $\pi$ (100 Hz) (2.50 uF)(10^-6 F / 1 uF)

     = 0.03925 A

For I₂,

I₂ = (25.0 V) 2 $\pi$ (1000 Hz) (2.50 uF)(10^-6 F / 1 uF)

     = 0.3925 A

For I₃,

I₃ = (25.0 V) 2 $\pi$ (1000 Hz) (2.50 uF)(10^-6 F / 1 uF)

     = 1.9625 A

Therefore, the rms current follows I₃ > I₂ > I₁.