Voltage drop across paralell resistor and capacitor

[teroenza]

Homework Statement

Find the voltage drop across a resistor and capacitor in parallel. I am trying to understand how to deal with this using complex numbers. I may have a completely wrong notion of complex impedance. I thought I could treat the complex impedance like resistance, then take the modulus or real part (I believe I know the math, but not which to apply).


I= 100 milli Amps
R= 1000 ohms
C= 0.001Farads
freq.= 60Hz=377rad/s

Homework Equations

Z_c=1/(i*omega*C)

R_eq= (R*Z_C)/(R+Z_C)

The Attempt at a Solution

Do I apply the standard resistors in parallel formula then take the real part of the modulus? Or do I have a completely wrong conception on complex impedance.

 

[gneill]

Homework Statement

Find the voltage drop across a resistor and capacitor in parallel. I am trying to understand how to deal with this using complex numbers. I may have a completely wrong notion of complex impedance. I thought I could treat the complex impedance like resistance, then take the modulus or real part (I believe I know the math, but not which to apply).


I= 100 milli Amps
R= 1000 ohms
C= 0.001Farads
freq.= 60Hz=377rad/s

Homework Equations

Z_c=1/(i*omega*C)

R_eq= (R*Z_C)/(R+Z_C)

The Attempt at a Solution

Do I apply the standard resistors in parallel formula then take the real part of the modulus? Or do I have a completely wrong conception on complex impedance.

Calculate the complex impedance as you've suggested using the 'usual' formula for resistors in parallel. Apply Ohm's law to find the (complex) voltage that will appear across the net impedance when driven by the 100mA current. The magnitude of that complex quantity should be what you're looking for.

 

[teroenza]

To be sure I fully understand, by magnitude you mean take the square root of (my complex quantity * its complex conjugate) ?

 

[gneill]

To be sure I fully understand, by magnitude you mean take the square root of (my complex quantity * its complex conjugate) ?

Yes.

 

[DeeNos]

I would like to first clarify that complex impedance is a valid concept in electrical engineering and is often used to analyze circuits containing both resistive and reactive elements. In this case, the voltage drop across a parallel combination of a resistor and capacitor can be calculated using the following formula:

V = I * R_eq

Where R_eq is the equivalent impedance of the parallel combination, given by:

R_eq = (R*Z_C) / (R+Z_C)

In this formula, R is the resistance of the resistor, and Z_C is the complex impedance of the capacitor given by:

Z_C = 1 / (i*omega*C)

Where i is the imaginary unit, omega is the angular frequency (in radians per second) and C is the capacitance in Farads.

To solve for the voltage drop, you can use the values provided in the problem:

I = 100 milli Amps = 0.1 Amps
R = 1000 ohms
C = 0.001 Farads
freq. = 60Hz = 377 rad/s

Plugging these values into the equations, we get:

Z_C = 1 / (i*377*0.001) = -2.65i ohms

R_eq = (1000*-2.65i) / (1000-2.65i) = -2.65i ohms

V = (0.1)*( -2.65i) = -0.265i volts

So, the voltage drop across the parallel combination of the resistor and capacitor is -0.265i volts. This means that the voltage is a complex number, with a real part of 0 and an imaginary part of -0.265 volts. This may seem counterintuitive, but it is a valid result when dealing with reactive components in circuits.

I hope this helps to clarify your understanding of complex impedance and its application in solving circuits with resistive and reactive elements in parallel. If you have any further questions, please feel free to ask.