Series R-L Circuits
- 1. Gandhinagar Institute of Technology(012) Active Learning Assignment Subject- EEE(2110005) Topic- Series R-L Circuits Branch-Computer Engineering C : C-2 Prepared By- Somai Rohankumar J.(201707000141) Guided By- Prof. Purv Mistry
- 2. • Series R-L Circuit Phase angle Initial Conditions Current Growth Steady-State-Current Current as a function of time during Growth calculations The time constant Energy and Power
- 3. Phase angle For Series R-L circuit, Z = R + jXL = R + j𝜔L and In the figure Z is shown by point H in Complex plane. From the figure it is clear that, In this circuit current lags behind the voltage in phase by 𝜹. Here the electric current
- 4. Series R-L Circuit Initial conditions S1 S2 ε L R a b c An R-L circuit is any circuit that contains both a resistor and an inductor. 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…then i = 0 and Ldt di initial Assume an ideal source
- 5. Series R-L Circuits Current GrowthS1 S2 ε LR a b c i 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 iRVab dt di bc LV L iR LL iR dt di dt di LiR If we apply Kirchhoff's Law to this circuit we get… 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”.
- 6. Series R-L Circuits Steady-State Current When the current reaches its final “steady-state” value, I, then di/dt = 0. I L R Ldt di final 0 Solving this equation for I… R I Do you recognize this? It is Ohm’s Law!!! So…when the current is at steady-state, the circuit would not behaves like inductor …unless it tries to change current values quickly. So, The steady-state current does NOT depend on L!
- 7. Series R-L Circuits Current as a function of time during Growth Calculations:- RL R L iR Ldt di i ti L Ri t L R i i di L R R R R R R e t dt ln 00 Let’s start with the equation we derived earlier from Kirchhoff's Law… Rearrange and integrate… Solve for i… tL R e R ti 1)( 0 𝑖 𝑑𝑖 𝑑𝑡 = 0 𝑡 −𝑅 𝐿 (i - 𝜀 𝑅 )
- 8. Series R-L Circuits The time constant:- tL R e R ti 1)( The time constant is the time at which the power of the “e” function is “-1”. Therefore, time constant is L/R R L
- 9. Series R-L Circuits Energy and Power dt di inductor resistor battery LiP RiP iP 2 dt di LiRii 2 Pbattery = Presistor + Pinductor S1 S2 ε LR a b c i