frutti said:Homework Statement
i need to find the Vs(t) and Vc(t)
http://img32.imageshack.us/img32/9071/circuiten.jpg
The Attempt at a Solution
since there is a switch i used two cases to find the Vc
one with switch on and switch off
switch on
http://img704.imageshack.us/img704/6180/switchon.jpg
and switch off
http://img265.imageshack.us/img265/3259/switchoff.jpg
but I am lost after this...
help me!
The initial conditions for a RC circuit with a switch can be determined by analyzing the circuit before the switch is closed. The voltage across the capacitor will be equal to the voltage across the resistor, and the current through the circuit will be zero. This can be represented as Vc(0) = Vs(0) and I(0) = 0.
The key difference is that when a switch is present, the initial conditions for the circuit are no longer zero. This means that the equations used to solve the circuit will include these initial conditions, and the solution will take into account the effects of the switch opening or closing.
To find Vc(t) and Vs(t) at a specific time, you can use the equations Vc(t) = Vc(0)e^(-t/RC) and Vs(t) = Vs(0)e^(-t/RC). Plug in the known values for Vc(0) and Vs(0), and solve for the desired time t. This will give you the voltage across the capacitor and the switch at that time.
When the switch is opened, the voltage across the capacitor will remain constant, while the voltage across the switch will drop to zero. When the switch is closed, the voltage across the capacitor will start to change, while the voltage across the switch will increase to the same value as the voltage source.
Yes, the initial conditions for a RC circuit with a switch can be negative. This will depend on the specific values of the circuit components and the position of the switch. It is important to carefully analyze the circuit to determine the correct initial conditions, as they will affect the solution for the circuit.