Calculating Current in Circuits With o.3μF Capacitor and 40Ω Resistor

[natural]

A o.3micro farad capacitor is connected across a 15V, variable frequency ac power supply. Find the current in the circuit when the frequency is a) 100herts (b) 100kilohertz

c) solve this question if thee 0.3 microfarad capacitor is replaced by a 40 ohm resistor.


My solution
I = wCV
a) 2*∏(pie)*100*o.3*10^-6*15
= 2.82*10^-3 A

b) 2*∏*100*103 *o.3*10^-6*15
= 2.82 A


Xc = 1/2πfC
therefore C = 1/2πfXc

C = 1/2*π*100*40
= 7.9*10-5

I=wVC
= 15*2*π*100*(7.9*10^-5)
= 0.74A

b) I=wVC
= 15*2*π*100*10^3*7.9*10^-5
=744A

did i do this correct? please let me know if I am going right.

 

[marcusl]

A o.3micro farad capacitor is connected across a 15V, variable frequency ac power supply. Find the current in the circuit when the frequency is a) 100herts (b) 100kilohertz

c) solve this question if thee 0.3 microfarad capacitor is replaced by a 40 ohm resistor.


My solution
I = wCV
a) 2*∏(pie)*100*o.3*10^-6*15
= 2.82*10^-3 A

b) 2*∏*100*103 *o.3*10^-6*15
= 2.82 A

This looks right.

Xc = 1/2πfC

You used this already above when you wrote "my solution"
(V=Xc*I --> I=V/Xc).

therefore C = 1/2πfXc

C = 1/2*π*100*40
= 7.9*10-5

I=wVC
= 15*2*π*100*(7.9*10^-5)
= 0.74A

b) I=wVC
= 15*2*π*100*10^3*7.9*10^-5
=744A

You're on the wrong track here. Use Ohms law to relate I, R and V.

 

[m2003]

Yes, your calculations appear to be correct. However, it would be helpful to provide the units for each value (e.g. Hz for frequency, Ω for resistance, and F for capacitance) and to use proper scientific notation (e.g. 2.82 x 10^-3 instead of 2.82 * 10^-3). Also, in the last part of your solution, you wrote "b)" instead of "c)". Overall, your approach and solution are correct. Keep up the good work!