Phase Angle between Voltage and Current

In summary, when a resistor is connected to an AC generator with a fixed frequency, there is a current of 0.465 A. When an inductor is connected, the current is 0.360 A. When both are connected in series, the impedance is 389.94 and the phase angle can be calculated using either the formula ɸ = cos⁻¹ (R/Z) or ɸ = tan⁻¹ (X/R). To find R, Ohm's Law can be used since the applied voltage and current are known.
  • #1
theintarnets
64
0

Homework Statement



"When only a resistor is connected across the terminals of an ac generator (111 V) that has a fixed frequency, there is a current of 0.465 A in the resistor. When only an inductor is connected across the terminals of this same generator, there is a current of 0.360 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, calculate the following.
(a) the impedance of the series combination


(b) the phase angle between the current and the voltage of the generator"

I got the impedance to be 389.94, but I don't know what other formulas to use to get the phase angle. Specifically, I don't know how to find XL.


Homework Equations



Phase angle = arctan(XL/R)
 
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  • #2
Nvm, I found another formula for phase angle = cos(R/Z)

I had the wrong variables written into the equation of Z, so I didn't realize I already calculated XL >.<
 
Last edited:
  • #3
I don't know how to find XL.

How would you find R? It is similar.
 
  • #4
theintarnets said:
Nvm, I found another formula for phase angle = cos(R/Z) ✗

phase angle ɸ = cos⁻¹ (R/Z)

this is identical with ɸ = tan⁻¹ (X/R)
 
  • #5
barryj said:
I don't know how to find XL.

How would you find R? It is similar.
Ohm's Law, you know the applied voltage and you know the current that flows.
 

Related to Phase Angle between Voltage and Current

What is the phase angle between voltage and current?

The phase angle between voltage and current is a measure of the difference in timing between the two waveforms. It represents the amount by which the current waveform leads or lags behind the voltage waveform.

Why is the phase angle between voltage and current important?

The phase angle between voltage and current is important because it provides information about the behavior of electrical circuits. It can help determine the power factor, which is a measure of the efficiency of a circuit, and can also indicate the presence of reactive components in the circuit.

How is the phase angle between voltage and current calculated?

The phase angle between voltage and current is calculated by finding the difference in phase between the voltage and current waveforms. This can be done by measuring the time delay between the zero crossings of the two waveforms, or by using mathematical formulas such as cosine or sine functions.

What does a positive or negative phase angle indicate?

A positive phase angle indicates that the current waveform is leading the voltage waveform, while a negative phase angle indicates that the current waveform is lagging behind the voltage waveform. This can provide information about the type of load in an electrical circuit, as resistive loads typically have a zero phase angle, while inductive or capacitive loads have positive or negative phase angles, respectively.

How does the phase angle affect power consumption?

The phase angle between voltage and current can affect power consumption by influencing the power factor of a circuit. A higher phase angle can result in a lower power factor, which means that the circuit is less efficient and more energy is wasted. This can lead to higher electricity bills and can also cause problems with power distribution systems.

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