Current through an inductor changes over time as it resists a sudden change. Below is the representation of current as the inverse of the inductance multiplied by the integral of the voltage with respect to time. After a long time the inductor will act as a short circuit.
Inductors are added just as resistors in series and parallel.
Below is an updated list of equations for RL, R, and RC circuits.
Below, being that we are told the circuit is opened at time zero to the right we see a sketch of ideal versus real world voltage over time.
Below we find an expression for the voltage as a function of time for an RC circuit.
The product of the resistance and capacitance is called the time constant. Below 1% of the initial voltage we may consider the capacitor "fully" discharged. Below, we find that at about 5 time constants we can consider the any capacitor discharged.
Using that current is the product of capacitance and derivative of voltage with respect to time we may find an expression for power. We used the expression of voltage we found above.
Enough of the symbols, let us plug in some numbers. Below, we use a simple RC circuit to find voltage and current over time.
Lab time!
Passive RC Circuit Response Lab
We are to observe the response of the circuit when a 5V supply voltage is removed suddenly.
Below, after about 5 time constants the capacitor is "low enough".
Below, we are to find the time constant for the RL circuit.
The graph is ugly to look at.
LAB #2!!!
Passive RL Circuit Natural Response
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