Finding Steady State Amplitude of Voltage Across Load Resistor

[CoolDude420]

Homework Statement

Find the steady state amplitude in volts of the voltage across the load resistor

Homework Equations

V source = 4sin4t
Resistors = both 1ohm
Cap = 1.414F
Inductor = 1.414H

The Attempt at a Solution

I converted to phasor domain first, then applied voltage division. Voltage across load resistor = voltage across capacitor(1.414 impedance.) The answer will be in rectangular form. To get the real-world amplitude, take the positive value of the Imaginary part of the complex number(part with j) which gives me 0.02.

We have been told that when converting to the real world from scalar always take imaginary part.

The correct answer is 0.12. I keep getting 0.02. I am noticing that the correct answer of 0.12 is the real part of my answer. No clue what I did wrong

 

[gneill]

I converted to phasor domain first, then applied voltage division. Voltage across load resistor = voltage across capacitor(1.414 impedance.) The answer will be in rectangular form. To get the real-world amplitude, take the positive value of the Imaginary part of the complex number(part with j) which gives me 0.02.

We have been told that when converting to the real world from scalar always take imaginary part.

That's not true unless you are working with the rotating phasor projections onto an axis. Usually this view of how phasor vectors are interpreted is superseded early on when the complex arithmetic representation is introduced. Since you're working with complex impedance and voltages and currents, you need to take the magnitude of the complex values to find their "real world" or time-domain magnitudes.

The correct answer is 0.12. I keep getting 0.02. I am noticing that the correct answer of 0.12 is the real part of my answer. No clue what I did wrong

You didn't include the load resistor in the voltage division. It parallels the capacitor and will draw current, too.

You can either replace that resistor and capacitor with an equivalent resistance before applying voltage division, or just go straight to nodal analysis and let it handle everything; there's only one essential node and it happens to correspond to the output voltage...

 

[CoolDude420]

That's not true unless you are working with the rotating phasor projections onto an axis. Usually this view of how phasor vectors are interpreted is superseded early on when the complex arithmetic representation is introduced. Since you're working with complex impedance and voltages and currents, you need to take the magnitude of the complex values to find their "real world" or time-domain magnitudes.

You didn't include the load resistor in the voltage division. It parallels the capacitor and will draw current, too.

You can either replace that resistor and capacitor with an equivalent resistance before applying voltage division, or just go straight to nodal analysis and let it handle everything; there's only one essential node and it happens to correspond to the output voltage...

This is taking years. soo many decimals. Is there a faster way?

 

[gneill]

This is taking years. soo many decimals. Is there a faster way?

Heh. It seems that every student has to go through this trial by algebra

My advice is to do much of the work symbolically, simplify algebraically, and plug in numbers at the end. That way you're not lugging around a boatload of decimal places over several pages of calculations. If there are repeated combinations of quantities, calculate once and give it a variable name. Use that as you carry on.

Finding an online complex math calculator or an app for your phone or tablet can help.