* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download RL Circuits - Humble ISD
Electric machine wikipedia , lookup
Mains electricity wikipedia , lookup
Thermal runaway wikipedia , lookup
Electronic engineering wikipedia , lookup
Skin effect wikipedia , lookup
Ground (electricity) wikipedia , lookup
Mercury-arc valve wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Electrical substation wikipedia , lookup
Electrical ballast wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Opto-isolator wikipedia , lookup
Surge protector wikipedia , lookup
Circuit breaker wikipedia , lookup
Rectiverter wikipedia , lookup
Alternating current wikipedia , lookup
Current source wikipedia , lookup
Earthing system wikipedia , lookup
Current mirror wikipedia , lookup
Flexible electronics wikipedia , lookup
Network analysis (electrical circuits) wikipedia , lookup
R-L Circuits R-L Circuits? What does the “L” stand for? Good Question! “L” stands for the self-inductance of an inductor measured in Henrys (H). So…What is an inductor? • An inductor is an electronic device that is put into a circuit to prevent rapid changes in current. • It is basically a coil of wire which uses the basic principles of electromagnetism and Lenz’s Law to store magnetic energy within the circuit for the purposes of stabilizing the current in that circuit. • The voltage drop across an inductor depends on the inductance value L and the rate of change of the current di/dt. V L di dt R-L Circuits The set up and initial conditions Assume an ideal source (r=0) ε An R-L circuit is any circuit that contains both a resistor and an inductor. S1 S2 a R b L c At time t = 0, we will close switch S1 to create a series circuit that includes the battery. The current will grow to a “steady-state” constant value at which the device will operate until powered off (i.e. the battery is removed) Initial conditions: At time t = 0…when S1 is closed…i = 0 and di dt initial L R-L Circuits Current Growth S ε 1 Note: we will use lower-case letters to represent time-varying quantities. S2 i a R b Vab iR L Vbc L dtdi c At time t = 0, S1 is closed, current, i, will grow at a rate that depends on the value of L until it reaches it’s final steady-state value, I If we apply Kirchoff’s Law to this circuit and do a little algebra we get… iR L di dt di dt LiR L iRL As “i” increases, “iR/L” also increases, so “di/dt” decreases until it reaches zero. At this time, the current has reached it’s final “steady-state” value “I”. R-L Circuits Steady-State Current ε S1 When the current reaches its final “steady-state” value, I, then di/dt = 0. S2 i a R b L c R di 0 I L L dt final Solving this equation for I… I R Do you recognize this? It is Ohm’s Law!!! So…when the current is at steady-state, the circuit behaves like the inductor is not there…unless it tries to change current values quickly! The steadystate current does NOT depend on L! R-L Circuits Current as a function of time during Growth The calculus and the algebra! ε S Let’s start with the equation we derived earlier from Kirchoff’s Law… 1 S 2 i a b R L c di dt L iR L R L i R Rearrange and integrate… i di 0 i R ln t R L 0 i R R i R R e dt R L RL t t Solve for i… i (t ) 1 e R RL t R-L Circuits The time constant! ε S1 i (t ) S2 i a b R L R L c 1 e R RL t The time constant is the time at which the power of the “e” function is “-1”. Therefore, time constant is L/R At time t = 2 time-constants, i = 0.86 I, and at time t = 5 time-constants, i = 0.99995 I Therefore, after approximately 5 time-constant intervals have passed, the circuit reaches its steady-state current. R-L Circuits Energy and Power ε Pbattery i S1 S2 Presistor i R 2 i a R b c L Pinductor Li i i R Li 2 di dt di dt