How can I find the DC component of an Output Sinusoidal Voltage?

In summary: Then divide it by 2 to get the DC component. In summary, the conversation discusses finding the DC component or equivalent of a time varying signal using the Root Mean Square method. The concept of RMS value is clarified, which is used for fluctuating physical quantities that are periodic in nature. The formula for finding the DC component is also discussed, with the general formula being preferred over a shortcut formula for MCQ exams.
  • #1
Rongeet Banerjee
45
6
Homework Statement
How can I find the RMS value of a DC Current?
Relevant Equations
Vrms=Vpeak/(2)½
IMG_20200822_121952466.jpg

I had previously solved this using Root Mean Square method by integrating the value of voltage from t=0 to t=T/2 and then from t=T/2 to t=T.Answer was Vo/2½.Yesterday I found this question👇🏾
15980792790661347500990.jpg

if I followed the previous approach then:
15980800547871983487461.jpg

15980801446431097768317.jpg

5 volts is not even in the option. How can I find the DC component of an Output Sinusoidal Voltage?
 
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  • #3
Rongeet Banerjee said:
Homework Statement:: How can I find the RMS value of a DC Current?
Relevant Equations:: Vrms=Vpeak/(2)½

I had previously solved this using Root Mean Square method
This gives you the dc "equivalent" of the time varying signal, not the dc "component" of it.
 
  • #4
Coming back to question 42,how can we find RMS value of a non alternating current?
 
  • #6
For DC, the actual value is the RMS value.
 
  • #7
Rongeet Banerjee said:
Coming back to question 42,how can we find RMS value of a non alternating current?
What is question 42?
Edit: Ok I can see that in your first image. Haven't you already solved it correctly? It is a non-alternating waveform. What else do you want to know?
Rongeet Banerjee said:
Ok.But isn't the average value of AC 2Vpeak/π.
No. The question mentions "a half wave" rectifier. What will the output voltage look like?

Also, ac in electricity usually means a periodic signal with both positive and negative halves (mostly sinusoidal signals). So the average value of ac is 0.
 
  • #8
cnh1995 said:
This gives you the dc "equivalent" of the time varying signal, not the dc "component" of it.
So basically when the question asked me to find RMS value they actually meant"DC equivalent".I got a bit confused because I had learned that only alternating currents have RMS values.So in reality is RMS value used for any fluctuating physical quantity?
 
  • #9
DC Component =(average of V from t=0 to t=T/2 + average of V fom t=T/2 to t=T) /2 i.e. =(20/π + 0)/2 =10/π .Is that the answer?
 
  • #10
Rongeet Banerjee said:
So in reality is RMS value used for any fluctuating physical quantity?
Yes, if they are fluctuating periodically.
Same is true for average value.
You compute rms and average values of a periodic signal and derive conclusions from it.
If the average of a periodic signal is 0, it is symmetric about the time axis (i.e. equal positive and negative parts).
If the average is non zero, it has a dc "component" in it which is making the positive and negative parts unequal.

If you are passing an alternating current through a resistor, the heat produced by the alternating current in its one cycle time is equal to the heat produced by its rms current(dc) in the same time. This means the rms current is the dc "equivalent" of the alternating current.
 
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  • #11
Rongeet Banerjee said:
DC Component =(average of V from t=0 to t=T/2 + average of V fom t=T/2 to t=T) /2 i.e. =(20/π + 0)/2 =10/π .Is that the answer?
Yes that is the answer, but I am not sure if the formula you wrote is correct. Is that some "trick" or "shortcut" considering the MCQ nature of some exam?
I prefer the general formula:
Average= integral of function/time period.
You can then split the integral as per the function behavior between t=0 to t=T.

In this case, your function is sinusoidal from 0 to T/2 and 0 from T/2 to T. You can split the integral accordingly and get the average value.
 

Related to How can I find the DC component of an Output Sinusoidal Voltage?

1. What is the DC component of an Output Sinusoidal Voltage?

The DC component of an Output Sinusoidal Voltage refers to the constant or average value of the voltage. It is the part of the voltage that does not change with time and remains at a constant level.

2. Why is it important to find the DC component of an Output Sinusoidal Voltage?

Knowing the DC component of an Output Sinusoidal Voltage is important because it helps in understanding the behavior and characteristics of the voltage signal. It also allows us to separate the AC and DC components, which can be useful in various applications.

3. How can I measure the DC component of an Output Sinusoidal Voltage?

The DC component of an Output Sinusoidal Voltage can be measured using a multimeter. Set the multimeter to DC voltage mode and connect it in parallel to the output voltage source. The reading on the multimeter will give you the value of the DC component.

4. Can the DC component of an Output Sinusoidal Voltage be negative?

Yes, the DC component of an Output Sinusoidal Voltage can be negative. This means that the average value of the voltage is below zero. It is important to consider the sign of the DC component when analyzing the voltage signal.

5. How does the frequency of the sinusoidal voltage affect the DC component?

The frequency of the sinusoidal voltage does not affect the DC component. The DC component remains constant regardless of the frequency of the voltage signal. However, the amplitude of the AC component may vary with frequency, which can indirectly affect the overall output voltage.

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