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Questions and Answers
What is the inductance L of the coil in Exercise 01?
Which of the following equations represents the voltage across the resistor U_R(t) in the circuit?
What is the expression for the maximum current I in the circuit in Exercise 01?
What does the time constant τ of the RL circuit represent?
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Which statement about the differential equation for the voltage across the resistor is true?
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When observing the curves on the oscilloscope, Curve 1 represents which parameter?
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What might be a plausible reason for the internal resistance r to be significant in the RL circuit?
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How is the energy stored in the coil related to the inductance L and the maximum current I?
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Study Notes
Exercise 1: RL Circuit Analysis
- Circuit configuration: A coil with inductance (L = 75 mH) and internal resistance (r = 11.5 Ω) is connected in series with a resistor (R = 68 Ω) and a constant voltage generator (E = 12 V).
- Differential equation: The differential equation governing the current (i(t)) in the coil is: L * di/dt + (R+r) * i(t) = E
- Solution form: The solution to the differential equation takes the form: i(t) = A + B*e^(-(R+r)/L)*t
- Maximum current: The maximum current (I) in the circuit is given by: I = E / (R+r)
- Voltage across the coil: The voltage across the coil (UL(t)) is expressed as: UL(t) = E / (R+r) * (r + R * e^(-(R+r)/L)*t)
- Voltage across the resistor: The voltage across the resistor (UR(t)) is expressed as: UR(t) = R*E / (R+r) * (1 - e^(-(R+r)/L)*t)
- Energy stored in the coil: The energy stored in the coil in steady state is given by: W = (1/2) * L * I^2
Exercise 2: RL Circuit Analysis with Oscilloscope Readings
- Circuit configuration: A coil with inductance (L) and internal resistance (r) is connected in series with a resistor (R = 200 Ω) and a constant voltage generator (Uo).
- Oscilloscope readings: Channel 1 traces the voltage across resistor (R), Channel 2 traces the voltage across the coil.
- Differential equation for UR(t): (L/(R+r)) * dUR/dt + UR(t) = (RE)/(R+r)
- Curve 1 analysis: Curve 1 in Figure 1 represents UR(t), the voltage across the resistor.
- Generator voltage: The generator voltage (Uo) can be determined by analyzing the steady-state value of UR(t) in Figure 1.
- Time constant: The time constant (τ) of the RL circuit is determined by the time it takes for UR(t) to reach approximately 63.2% of its final value in Figure 1.
- Steady-state current: The steady-state current (I) in the RL circuit is calculated as I = Uo / (R+r)
- Inductance: The inductance (L) of the coil is calculated using the time constant: L = τ * (R+r)
- Internal resistance: The internal resistance (r) of the coil is calculated using the steady-state current and the generator voltage: r = Uo/I - R
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Description
Test your knowledge on RL circuit analysis with this quiz. Questions cover circuit configurations, differential equations, current calculations, and energy stored in coils. Ensure you understand the principles and mathematical solutions involved in RL circuits.
