Analysis of RLC Circuit v(t): Find Voltage with Ohm's Law

In summary, the conversation discusses a circuit that is found to be critically dampened with w0 and a0 equal to 20. The equation for V(inf) is calculated using current divider and ohm's law, resulting in a value of 36V. The circuit is then analyzed at t<0, t>0, and t=inf, with the differential equation being the focus. It is suggested to substitute the resistors and current source with a Thevenin equivalent to calculate V(inf) correctly, resulting in a value of 4V. The calculation for the current through the switch and V(0-) is also provided.
  • #1
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So I found the circuit is series, w0 and a0 equal 20 so it is critically dampened. For V(inf) I used current divider to get the equation (.1 A *120 ohm)/40 ohm = .3 A. Then I used ohms law to find v(t) = .3*120 = 36 V.

I then wrote down the circuit at t<0, t>0, and t=inf. I am stuck at this point.
 
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  • #2
so t<0 will give you your initial conditions
t inf will give you your steady state value.
T>0 will give you the differential equation that you are looking for.

write out the differential equation first and solve it, either in time or frequency domains
 
  • #3
Your V(inf) calculation is wrong. Substitute the two resistors to the right and the current source with a Thevenin equivalent: 40Ω in series with a 4V voltage source.
So V(inf) = 4V.

The current through the switch, I(0-) will be (4V - (-6V) ) / ( 40Ω + 40Ω ) = 0.125A (from right to left ).

So V(0-) = -6V + 0.125A*40Ω = -1V.
 

Related to Analysis of RLC Circuit v(t): Find Voltage with Ohm's Law

1. How do you determine the voltage in an RLC circuit using Ohm's Law?

To determine the voltage in an RLC circuit using Ohm's Law, you will need to know the values of the resistance (R), inductance (L), and capacitance (C) in the circuit. Once you have these values, you can use the formula V = IR, where V is the voltage, I is the current, and R is the resistance. This formula can be applied to each individual component in the circuit to calculate the voltage across each one.

2. What is an RLC circuit and how does it work?

An RLC circuit is an electrical circuit that consists of a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. These three components interact with each other to create a phenomenon known as resonance. In a series RLC circuit, when the frequency of the input voltage matches the natural frequency of the circuit, the voltage across the components becomes maximum, while the current becomes minimum. This phenomenon is known as resonance and is used in many applications, such as radio communication and tuning circuits.

3. Can you use Ohm's Law to find the voltage in any type of circuit?

Yes, Ohm's Law can be used to find the voltage in any type of circuit, as long as the values of the resistance, current, and voltage are known. However, in more complex circuits, such as RLC circuits, the calculations may be more complicated and require the use of other formulas or techniques.

4. What is the significance of using Ohm's Law in the analysis of RLC circuits?

Ohm's Law is a fundamental law in physics that relates the voltage, current, and resistance in a circuit. In RLC circuits, it is used to determine the voltage across each component, which is essential in understanding the behavior of the circuit and its performance. Ohm's Law also allows for the calculation of other important parameters, such as power and energy, which are crucial in the design and analysis of electrical circuits.

5. What are the limitations of using Ohm's Law in analyzing RLC circuits?

One of the main limitations of using Ohm's Law in analyzing RLC circuits is that it assumes the components in the circuit are linear and do not change with time. In reality, components such as inductors and capacitors can exhibit non-linear behavior and may change with time, which can affect the accuracy of the analysis. In these cases, more complex mathematical techniques, such as differential equations, may be needed to accurately analyze the circuit.

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