Chapter 30 - Magnetic Induction - FSU Physics Department

RL circuitsA circuit that contains a resistor, R and aninductor, L is called a RL circuit. Because it takestime for the magnetic fields in an inductor to buildup, the current that flows through a RL circuitdepends on time when the switch is turned on.Using Kirchhoff’s rule,ξ odI− IR − Ldt= 0The solution for the above equation isLet’s examine the solution in the two extremecases, (1) at t = 0 and (2) when t →∞.Case 1: t = 0 Immediately, after the switch isclosed, the current is zero. This means that thereis no voltage across the resistor. However, therate of current increase at t = 0 is then⎛ dI⎜⎝ dtIf⎞⎟⎠t=0ξo=Rξo=LCase 2: t→∞ As the current increases the voltageacross R becomes non-zero. When t→∞, the rateof current increase approaches 0, i.e., the finalcurrent then becomes−RtL−tτ( 1−e ) = I ( − e )ξoI =f1Rwhere τ = L/R is called the time constant(similarly in concept to the time constant in RCcircuits.)PHY2049C - Prof. Ng 6