Finding delay angle ,Vrms, Irms using AC voltage/ load resistor

In summary, the conversation discusses the expression for RMS voltage in a light dimmer circuit connected to 240V AC main, and how to calculate the range of values of the delay angle α. The equations used include P=Vrms^2/2∏R (∏-α+1/2sin(2α)), where R is the load resistance, Vrms is the amplitude of supply voltage, and α is the delay. If the nominal ratings are 240 V AC and 40 W, the RMS voltage can be calculated as 169.7 V and the delay angle α can be solved for using the given equation.
  • #1
pokie_panda
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Homework Statement



From the average power consumed by the lamp in a light dimmer circuit connected to 240V AC main,
What is the expression for RMS voltage,
calculate the range of values of the delay angle α,(i)RMS voltage (ii)RMS current in the lamp, (iii) the average power if its nominal ratings are 240 V AC, 40 W.

Homework Equations



P=Vrms^2/2∏R (∏-α+1/2sin(2α))
R= load resistance
Vrms= amplitude of supply voltage
α=delay

The Attempt at a Solution


This is where I'm not sure ,
if we have the nominal ratings of 240V AC and 40 W,
we know that
Vrms = 240/sqrt(2)
=169.7
Then from the equation above solve for α
 
Last edited:
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  • #2
Don't worry i figured it out
 

1. How do you calculate the delay angle for an AC voltage?

The delay angle for an AC voltage can be calculated by using the formula: delay angle = arccos(PF), where PF is the power factor. The power factor can be determined by dividing the real power (P) by the apparent power (S).

2. What is the significance of finding the delay angle in AC circuits?

The delay angle is an important parameter in AC circuits as it represents the phase difference between the voltage and current waveforms. It is used to calculate the power factor and helps in understanding the efficiency of the circuit.

3. How do you find the RMS voltage in an AC circuit?

The RMS (Root Mean Square) voltage in an AC circuit can be calculated by using the formula: Vrms = Vmax / √2, where Vmax is the maximum voltage value in the circuit. This value is important as it represents the equivalent DC voltage that would produce the same amount of power in a circuit.

4. What is the significance of finding the RMS current in an AC circuit?

The RMS (Root Mean Square) current in an AC circuit is important as it represents the equivalent DC current that would produce the same amount of power in a circuit. It is also used to determine the power dissipated in a load resistor and to calculate the overall efficiency of the circuit.

5. How do you use load resistors to find the delay angle, Vrms, and Irms in an AC circuit?

To find the delay angle in an AC circuit, a load resistor can be connected in series with the circuit and the voltage and current waveforms can be measured using an oscilloscope. The delay angle can then be calculated using the formula mentioned in question 1. To find the Vrms and Irms, the load resistor can be connected in parallel with the circuit and the voltage and current can be measured across it. The Vrms can be calculated using the formula in question 3 and the Irms can be calculated by dividing the Vrms by the value of the load resistor.

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