For the circuit shown above, determine the following:i. Complete the auxiliary equation for the differential equation for \(i(t)\) for \(t>0\)?\[ 1.25s^2 + \_\_\_\_ = 0 \]ii. What is the current in the inductor before the switch is opened?\[ \_\_\_\_ \, \text{A} \]iii. What is the magnitude of the voltage across the capacitor just before the switch is opened?\[ \_\_\_\_ \, \text{V} \] The diagram represents an electrical circuit containing various components. Here's a detailed explanation:**Components and Configuration:**1. **Voltage Sources:** - A 12V voltage source on the left side. - A 6V voltage source in the middle of the circuit.2. **Resistors:** - A 6Ω resistor is connected in series with the top path of the circuit. - A 1.5Ω resistor is connected in series with the right path of the circuit.3. **Inductor:** - A 1.25 H inductor is placed in the path with the 12V source.4. **Capacitor:** - A 0.1 F capacitor is connected in the branch with the 1.5Ω resistor.5. **Switch:** - A switch is located between the paths containing the resistors and is initially open (indicated by \( t = 0 \)). Its direction is curved towards the 1.5Ω resistor.6. **Current:** - The current \( i(t) \) is marked on the left path, suggesting it flows through the 12V source and the inductor.**Circuit Analysis:**- This circuit appears to be suited for transient analysis at the moment when the switch is closed (\( t = 0 \)).- The combination of resistors, inductor, and capacitor indicates that this could be an RLC circuit, often used to demonstrate the behavior of reactive components in AC and transient states.By analyzing this setup, one can explore concepts such as time constants, reactive behavior, energy storage, and dissipation in electrical circuits.

Apply KVL in loop to find current i in terms in s domain , using current equation determine auxiliary equation. Inductor does not allow sudden changes in current i.e current in inductor at just t=0- is same as current just t=0. Capacitor does not allow sudden changes in voltage .

Engineering

Electrical Engineering

For the circuit shown above, determine the following: i. Complete the auxillary equation for the differential equation for i(t) for t>0? 1.25s2+ =0 ii. What is the current in the inductor before the switch is opened? iii. What is the magnitude of the voltage across the capacitor just before the switch is opened)?

For the circuit shown above, determine the following: i. Complete the auxillary equation for the differential equation for i(t) for t>0? 1.25s2+ =0 ii. What is the current in the inductor before the switch is opened? iii. What is the magnitude of the voltage across the capacitor just before the switch is opened)?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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a. Determine time constant(t). b. Write the mathematical expression for the current iL after the switch is closed at t = 0 s. c. Write the mathematical expression for VL and VR after the switch is closed at t = 0 s. d. Determine iL and VL at t = 1t, 3t, and 5t e. Sketch the waveforms of iL, VL, and VR for the. storage phase. Please answer all subpart in typing format please Not only three subpart I will dislike Please
3. For the circuit, (i) Find the voltage vc and the current ic if the capacitor was initially uncharged and the switch is thrown into position A. (ii) Find the voltage vc and the current ic if the switch is thrown into position B. (iii) Plot the waveforms for the questions (i) and (ii) for both the voltage vc and the current ic. Mark the time constant for part (i) and part (ii) in the waveforms with the corresponding values for current and voltage. A ww ic 20 kΩ B + + 12 V Vc. R, •10 kΩ 0.05 μF
19. After closing of the switch in this circuit (immediately below), what will be the steady-state current through the switch? Assume an ideal inductor. a. 10 mA b. 11 mA e. OmA d. 1mA 10V 10k2 1kQ 10mH
A capacitor is connected to an electrical circuit as shown in the image. The initial voltage of the capacitor will be that obtained when fully charged with all four switches closed. Then the switches that are required for it to start downloading are opened. It is known that after 0.1 s in its discharge process, the voltage on the capacitor is 20% of the voltage it initially had. Questions: 1. Explain how the initial voltage of the capacitor can be calculated.2. Indicate which switches are necessary to start the discharge of the capacitor and why.
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4. Why do we examine the behavior of an inductor when the current through it is changing? 5. What is the definition of the time constant? The definition of the time constant is I
A capacitor is connected to an electrical circuit as shown in the image. The initial voltage of the capacitor will be that obtained when fully charged with all four switches closed. Then the switches that are required for it to start downloading are opened. It is known that after 0.1 s in its discharge process, the voltage on the capacitor is 20% of the voltage it initially had. Questions: 1. Explain how the initial voltage of the capacitor can be calculated.2. Calculate the initial voltage of the capacitor before it begins to discharge.3. Say characteristic switches are necessary to initiate the discharge of the capacitor and why.4. Calculate the value of the capacitance.
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An initially charged capacitor has an initial voltage of Vo=53 Vand a capacitance ofC=175μFand it is connected to a resistor of resistance R=4.85kΩas shown in the figure below. The switch is closed at t=0. Determine the current running in the circuit one time constant after the switch is closed. Express your answer in units of mA using one decimal place.