Identifying 2 Elements in an AC Circuit: R & L

In summary, the problem involves a circuit with two elements, resistance and inductance, connected to a 120V, 60Hz AC generator. The current of 6.4A lags the voltage by 30o. Using the equations for voltage, frequency, current, and phase angle, we can calculate the values for resistance and inductance to be 18.75Ω and 0.028 henry respectively. The reasoning and calculations used are accurate, with a calculated value of 0.02869 henry when using more digits of pi.
  • #1
zakaqel
10
0

Homework Statement



A circuit contains only two of the three elements L,C ,R. When connected to a 120 V , 60 HZ ac generator, the current of 6.4 A lags the voltage by 30o. What are the two elements and their values?


Homework Equations





The Attempt at a Solution



given E = 120v,
f = 60Hz,
i = 6.4A,
φ =300
From the problem current lags voltage so this is a circuit containing resistance and inductance
inthis circuit , tanφ = ωL/R
R = E/i = 120/6.4 = 18.75Ω
L = tanφR/ω = tan300*18.75/2*3.14 *60 =0.028 henry


Is this reasoning correct?
 
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  • #2
The technique looks good.

I get a calculated value of .02869

I used more digits of pi.
 
  • #3
Thank you so much for the help!
 

1. What is an AC circuit?

An AC (alternating current) circuit is a type of electrical circuit in which the current periodically changes direction. This is different from a DC (direct current) circuit, in which the current flows in only one direction.

2. How do you identify the two elements in an AC circuit?

The two elements in an AC circuit are resistance (R) and inductance (L). Resistance measures the opposition to current flow, while inductance measures the tendency of a conductor to resist changes in current. These two elements can be identified by using Ohm's Law and the formula for inductive reactance.

3. What is Ohm's Law?

Ohm's Law is a fundamental law in electrical circuits that states the relationship between voltage, current, and resistance. It states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. It can be written as V = IR, where V is voltage, I is current, and R is resistance.

4. How do you calculate inductive reactance?

Inductive reactance (XL) is a measure of the opposition to current flow caused by inductance in an AC circuit. It can be calculated using the formula XL = 2πfL, where f is the frequency of the AC current in hertz and L is the inductance in henrys.

5. Why is it important to identify R and L in an AC circuit?

Identifying R and L in an AC circuit is important for understanding and analyzing the behavior of the circuit. These two elements affect the flow of current and can impact the performance and efficiency of the circuit. By knowing the values of R and L, engineers and scientists can make informed decisions about how to design and optimize the circuit for a specific purpose.

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