Calculating Resistance and Input Voltage in an RL Circuit with AC Generator

In summary, A 60 Hz AC voltage is applied to a series circuit containing a resistance of R and an inductance of 1.4 H. The voltage across the resistor is 30V and the voltage across the inductor is 40V. To find the resistance R, the equation I= \xi/ \sqrt{}R^2+X^2 is used, where I is the current and \xi is the voltage. To find the AC input voltage, the formula V=\sqrt{}40^2+30^2=50 V is used where V is the voltage across the inductor.
  • #1
nns91
301
1

Homework Statement



A resistance R and a 1.4 H inductance are in series across a 60 Hz AC voltage. The voltage across the resistor is 30V and the voltage across the inductor is 40V.
(a). What is the resistance R ?
(b). What is the AC input voltage ?

Homework Equations



[tex]\xi[/tex]=I*Z

The Attempt at a Solution



(a).So far I have I=[tex]\xi[/tex]/ [tex]\sqrt{}R^2+X^2[/tex]

How do I proceed from here ? Do I use I= [tex]\xi[/tex]/ [tex]\omega[/tex]L to find the current then substitute back to the first equation to solve for R ?

(b). I calculated V=[tex]\sqrt{}40^2+30^2[/tex]=50 V. Is this correct ?
 
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  • #2
I mean X(L)^2 not XL^2
 

Related to Calculating Resistance and Input Voltage in an RL Circuit with AC Generator

1. What is an RL circuit with AC generator?

An RL circuit with AC generator is a type of electrical circuit that consists of a resistor (R) and an inductor (L) connected in series, with an alternating current (AC) generator as the power source. It is used to study the behavior of electricity in a circuit with both resistance and inductance.

2. What is the purpose of using an AC generator in an RL circuit?

The AC generator in an RL circuit is used to provide a source of alternating current, which enables the study of the circuit's behavior under changing voltage and current conditions. This allows for the analysis of the effects of inductance on the current and voltage in the circuit.

3. How does an RL circuit with AC generator differ from a DC circuit?

An RL circuit with AC generator differs from a DC circuit in that the AC generator provides an alternating current, while a DC circuit is powered by a direct current source. Additionally, the behavior of an RL circuit is influenced by the inductor's ability to store energy, while a DC circuit is not affected by inductance.

4. What factors affect the behavior of an RL circuit with AC generator?

The behavior of an RL circuit with AC generator is affected by several factors, including the resistance (R) and inductance (L) values of the components, the frequency of the AC generator, and the amplitude of the alternating current. The phase difference between the voltage and current in the circuit also plays a role in its behavior.

5. What are some real-world applications of an RL circuit with AC generator?

RL circuits with AC generators have many practical applications, such as in power generation and distribution systems, electric motors, and electronic filters. They are also commonly used in electronic devices, such as radios, televisions, and computers, to regulate and control the flow of electricity.

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