A generator delivers an AC voltage of the form Δv =(82 V) sin (75πt) to a capacitor. Themaximum current in the circuit is 1.00A. Find the following. (a) rms voltage of the generator
1 V
(b) frequency of the generator
2 Hz
(c) rms current
3 A
(d) reactance
4 Ω
(e) value of the capacitance
5 F

1. 57.99V

2. 37.5Hz

3. 0.7072A

4. 82 ohms

5. 5.18x10^-5F

Explanation:

In answer to this question, we have the Standard equation of AC emf to be

V = V0 x sin ωt

We have

V0 = 82V,

ω = 75π

1.

RMS Voltage =

V0/√2 = 82 /√2

= 82/1.414

= 57.99V

2.

ω = 2π* f

75π = 2πf

Frequency,f = 75π/2π

= 235.5/6.28

= 37.5 Hz

3.

RMS current

= Imax/√2

= 1.00/1.414

= 0.7072A

4.

Reactance

= Vrms/ Irms

= 57.99/0.7072

= 81.999

= 82.0 Ω

5.

Reactance = 1/ ω x C

Reactance = 82

ω = 75π

We put these values into the equation above and make c the subject of the formula

C = 1/82.0 x 75π

C = 1/ 82.0 x 75 x 3.14

C = 1/19311

Capacitance = 5.18x10^-5F