Solve Impedance Problem: 50nF Capacitor & 47kΩ Resistor

[k31453]

Homework Statement

A circuit consists of a 50nF capacitor in series with a 47kΩ resistor. An AC voltage of 120Vrms at
350Hz is applied to the circuit.

(a) Determine the current flowing through the circuit.
(b) Sketch the impedance diagram for the circuit at this frequency.

Homework Equations

Xc , diagram , V = IZ

The Attempt at a Solution

First i found Xc = 1/2* pi* f * C

Then i did impedence diagram to find z and then use V = IZ to find Z

I got the answer: 2.51mA

But why it says answer is : 3.545sin(700π+11^0)mA ?

 

[ehild]

Homework Statement

A circuit consists of a 50nF capacitor in series with a 47kΩ resistor. An AC voltage of 120Vrms at
350Hz is applied to the circuit.

(a) Determine the current flowing through the circuit.
(b) Sketch the impedance diagram for the circuit at this frequency.

Homework Equations

Xc , diagram , V = IZ

The Attempt at a Solution

First i found Xc = 1/2* pi* f * C

That is wrong. Check your lecture notes or books.


ehild

 

[k31453]

That is wrong. Check your lecture notes or books.


ehild

isnt it Xc = 1/ angular freq.* C ??

 

[ehild]

isnt it Xc = 1/ angular freq.* C ??

Xc = 1/ angular freq.* C means 1/angular frequency, multiplied by C. Use parentheses: Xc=-1/(ωC) and do not forget, that Xc is negative.

Show your work in detail.

ehild

 

[Nickie]

Your calculation of 2.51mA for the current flowing through the circuit is correct. However, the given answer of 3.545sin(700π+11^0)mA is not the same thing. It is giving the current as a sinusoidal function with a phase angle of 11 degrees, rather than a constant value of 2.51mA. This may be a more accurate representation of the current in the circuit, taking into account the AC voltage applied.