A 80 kHz sinusoidal voltage has zero phase angle and a maximum amplitude of 25 mV. When this voltage is applied across the terminals of a capacitor, the resulting steady-state current has a maximum amplitude of 628.32 μA. a) What is the frequency of the current in radians per second? b) What is the phase angle of the current? c) What is the capacitive reactance of the capacitor? d) What is the capacitance of the capacitor in microfarads? e) What is the impedance of the capacitor?

a. 1.6π*10⁵rads/secs

b. 90⁰

c. 39.8ohms

d. 0.04997μF

e. 39.8ohms

Explanation:

a. From the question, the frequency is given as 80KHz. The angular frequency is expressed as

W=2πf

w=2*π*80000

w=1.6π*10⁵rads/secs

b. To determine the phase angle of the current, from general ohms law

I=V/Y

where Y is the capacitive reactance

expressed as

Y=1/wc.

Also in an RC circuit the voltage lags the current

Hence expressing in polar form,

I=0.025wc< (0+90)

I=0.025wc<90⁰

The required phase angle is 90⁰

c. from the equation above the magnitude is

I=0.025wc,

if we substitute the value of the current as 628.3μA and w=1.6π*10⁵rads/secs

we have

C = (628.3μ) / (0.025*1.6π*10⁵)

C=0.04997μF

The reactance is expressed as

Y=1/wc

Y=1 / (1.6π*10⁵*0.04997*10⁻⁶)

Y=39.8ohms

d. as calculated above the capacitance of the capacitor is

0.04997μF.

e. since the impedance is express mathematically as

Z=√ (Y²) = 39.8ohms