- #1
theBEAST
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Homework Statement
The Attempt at a Solution
I tried two different methods and came to an odd conclusion:
aralbrec said:In method 1, Voc is not zero. No current flows so Voc = 12. If Voc were zero, you would be claiming the open circuit behaved like a short circuit and there would be a path for current to flow through Voc to the resistors.
In method 2, you are mixing up the conditions at t=0- and t=0+. At t=0-, the switch is closed and the capacitor is open (no current flows through it). At t=0+, the switch is open but the capacitor is in there because current will flow through it. The connection between t=0- and t=0+ is that currents and voltages cannot instantly change so the initial condition prior to the switch opening will be the same as after it opens.
theBEAST said:Wait, why is Voc = 12? If there's no current through the three resistors on the left loop then the voltage would be zero wouldn't it?
An RC circuit is a type of circuit that contains a resistor (R) and a capacitor (C) connected in series or parallel. It is commonly used in electronic devices to filter or shape electrical signals.
Differential equations are used to describe the behavior of dynamic systems, such as RC circuits. They take into account the changing values of voltage and current over time, making them an effective tool for analyzing and solving complex circuits.
The steps for solving an RC circuit using differential equations are as follows:
1. Write the differential equation for the circuit using Kirchhoff's voltage law and Ohm's law.
2. Simplify the equation by substituting any known values and rearranging terms.
3. Solve the differential equation using integration to find the general solution.
4. Apply initial conditions, such as the initial voltage or current values, to find the particular solution.
5. Use the particular solution to find the voltage or current at any given time.
Solving RC circuits using differential equations is important in the design and analysis of electronic circuits. It can help engineers predict the behavior of a circuit and make necessary adjustments to optimize its performance. It is also used in fields such as telecommunications, control systems, and signal processing.
Yes, there are other methods for solving RC circuits, such as using phasors, Laplace transforms, or computer simulations. However, differential equations are considered the most accurate and versatile method, and are commonly used in engineering and scientific applications.