Calculating Vac in a Half Wave Rectifier Circuit with Capacitor

In summary, to solve for Vac in a half wave rectifier with a capacitor, use the expression Vout=Vdc + Vac. This can be done by assuming a straight line between t=0 and t=T and formulating a y=mx+b equation for Vout, where Vdc can be calculated using Vdc= Vp - VpT/2RC. Eventually, Vac can be used to calculate Vrms and ripple factor.
  • #1
kstopp
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Homework Statement



Using the approximate triangular output shown and Vdc previously calculated, use the expression Vout=Vdc + Vac to solve for Vac. Find an expression for Vac that is valid from t=0 to t=T. Your expression should be in terms of Vp,R,C,T and t.

The circuit is a half wave rectifier with a capacitor.

Eventually I am trying to calculate ripple factor but I need the Vac to calculate Vrms and then onto calculating ripple = Vac rms / Vdc

Homework Equations



Vdc= Vp - VpT/2RC where Vp= voltage at peak

Vout=Vdc + Vac


The Attempt at a Solution



I am not sure what I am supposed to be using for V out. I was given Vin=Vocosωt where T=2∏/ω is the period of the input signal.

Am I supposed to use Vpcosωt for my Vout?
 
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  • #2
I figured it out, I had to assume that I was looking at a straight line between t=0 and t=T. Then formulate a y=mx+b for the line. That was my Vout I was looking for.
 

1. What is a half wave rectifier circuit?

A half wave rectifier circuit is an electronic circuit that converts alternating current (AC) to direct current (DC) by only allowing the positive half of the AC waveform to pass through. This results in a pulsating DC output.

2. How does a half wave rectifier circuit work?

A half wave rectifier circuit typically consists of a diode, a load resistor, and a transformer. The diode acts as a one-way valve, allowing current to flow in only one direction. When the AC voltage is positive, the diode conducts and allows current to flow through the load resistor, resulting in a positive half cycle of the waveform. When the AC voltage is negative, the diode does not conduct and no current flows through the circuit, resulting in a zero output.

3. What is the advantage of using a half wave rectifier circuit?

The main advantage of a half wave rectifier circuit is its simplicity and cost-effectiveness. It requires only a single diode and a load resistor, making it easy to design and implement. However, it has a lower efficiency and produces a pulsating DC output, which may not be suitable for some applications.

4. What are the applications of a half wave rectifier circuit?

A half wave rectifier circuit is commonly used in small electronic devices such as radios, power supplies, and battery chargers. It can also be used in circuits that require low power and do not need a constant DC output, such as LED lights and sensors.

5. How can the efficiency of a half wave rectifier circuit be improved?

The efficiency of a half wave rectifier circuit can be improved by using a full wave rectifier circuit, which allows both the positive and negative half cycles of the AC waveform to be converted to DC. Additionally, using a smoothing capacitor can reduce the amount of ripple in the output, resulting in a more stable DC output.

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