![]() ![]() You may or may not needall these variables. Use this last expression to obtain an expression for. Integrating both sides of this equation yields Using these equations, we can get, aftersome rearranging of the variables and making the subsitution, Note that we can use the loop rule (goingaround counterclockwise): Now that we have a feel for the state of the circuit in its steadystate, let us obtain the expression for the current in the circuitas a function of time. What is the voltage across the resistor in the steady state? What is the voltage across the inductor in the steady state? What is thecurrent in the circuit in the steady state? There is no induced EMF because the initial value of the current iszero.Įventually, the process approaches a steady state. Shortly after the switch is closed, what is the direction of theinduced EMF in the inductor? There is no current because the inductor does not allow the currentto increase from its initial zero value. Shortly after the switch is closed, what is the direction of thecurrent in the circuit? Immediately after the switch is closed, what is the voltage acrossthe inductor? ![]() Immediately after the switch is closed, what is the voltage acrossthe resistor? Immediately after the switch is closed, what is the current in thecircuit? Note that at any time during the process, Kirchhoff's loop ruleholds and is, indeed, helpful: In our further analysis, lowercaseletters will denote the instantaneous values of various quantities,whereas capital letters will denote the maximum values of therespective quantities. ![]() Let us start by analyzing the process that takes place after switchis closed (switch remains open). The wires (including the ones thatmake up the inductor) are also assumed to have negligibleresistance. Due to a fundamental property of an inductorto mitigate any "externally imposed" change in current, the currentin such a circuit changes gradually when a switch is closed oropened.Ĭonsider a series circuit containing a resistor of resistance andan inductor of inductance connected to a source of emf andnegligible internal resistance. This is not the case for a circuitcontaining inductors. In a circuit containing only resistors, the basic (though notnecessarily explicit) assumption is that the current reaches itssteady-state value instantly. ![]()
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