a series lr circuit contains an emf source of 14v

Lyra Rowan

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30-09-2024

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In the realm of electrical engineering, understanding the behavior of various circuit configurations is essential. One significant type of circuit is the Series LR circuit, which comprises a resistor (R), an inductor (L), and an electromotive force (EMF) source. In this article, we will focus on a Series LR circuit with an EMF source of 14V, exploring its characteristics, behavior over time, and practical applications.

What is a Series LR Circuit?

A Series LR circuit consists of:

• Inductor (L): A passive component that stores energy in its magnetic field when electric current flows through it.
• Resistor (R): A passive component that opposes the flow of current, converting electrical energy into heat.
• EMF Source: Provides the voltage (in this case, 14V) necessary to drive current through the circuit.

Key Features of a Series LR Circuit

1. Time Constant (τ): The time constant of an LR circuit is given by the formula: [ \tau = \frac{L}{R} ] It indicates how quickly the current reaches its maximum value after the circuit is energized. The larger the time constant, the slower the current rises.

2. Current Behavior: When the circuit is first connected, the current (I) increases exponentially and can be described by the equation: [ I(t) = \frac{V}{R} \left(1 - e^{-\frac{R}{L}t}\right) ] where:

   • (V) is the EMF (14V in our case),
   • (R) is the resistance,
   • (L) is the inductance,
   • (t) is the time, and
   • (e) is the base of the natural logarithm.

3. Voltage Across Components:

   • The voltage drop across the resistor can be calculated using Ohm's Law: [ V_R = I \cdot R ]
   • The voltage across the inductor is given by: [ V_L = L \frac{dI}{dt} ]

Analyzing a 14V Series LR Circuit

Let's consider a practical example of a Series LR circuit with a 14V EMF source, a resistor of 10Ω, and an inductor of 0.5H.

1. Calculating Time Constant (τ): [ \tau = \frac{L}{R} = \frac{0.5H}{10Ω} = 0.05s ] This indicates that the current will reach approximately 63.2% of its maximum value in 0.05 seconds.

2. Determining Maximum Current: The maximum current (I_max) can be calculated as: [ I_{max} = \frac{V}{R} = \frac{14V}{10Ω} = 1.4A ]

3. Current Over Time: To see how current changes over time, substituting values into the current equation:

   • After 0.05 seconds: [ I(0.05s) = \frac{14V}{10Ω} \left(1 - e^{-\frac{10Ω}{0.5H} \cdot 0.05s}\right) = 0.865A ]
   • After 0.1 seconds: [ I(0.1s) \approx 1.2A ]
   • After 0.2 seconds, the current will be very close to the maximum 1.4A.

Practical Applications of Series LR Circuits

1. Filtering Applications: Series LR circuits are commonly found in audio equipment as low-pass filters, allowing low-frequency signals to pass while attenuating high-frequency signals.

2. Electrical Motors: Inductors are critical components in motors, where they help manage current and enhance performance.

3. Energy Storage: Inductors in Series LR circuits can store energy temporarily, making them useful in power supplies and oscillators.

Conclusion

A Series LR circuit powered by a 14V EMF source showcases fundamental principles of electromagnetism and circuit theory. Understanding the dynamics of current, resistance, and inductance is vital for engineers and hobbyists alike. By examining such circuits, we can better appreciate their significance in practical applications, from filtering signals to managing energy in electronic devices.

References

Content from Brainly contributed valuable insights to this article, specifically regarding the understanding of LR circuits. Thank you to the contributors who provided foundational knowledge on this topic.

By utilizing a mix of theory and practical application, this article serves as a comprehensive guide to Series LR circuits, particularly those powered by a 14V EMF source. If you have further questions or need clarification on specific aspects, feel free to reach out!