Series R-L Circuits

Series RL circuits for ALA

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. Contents 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 + jX L = R + j 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 . Here the electric current  

4. Series R-L Circuit Initial conditions S 1 S 2 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 Assume an ideal source

5. Series R-L Circuits Current Growth S 1 S 2 ε L R a b c i At time t = 0, S 1 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 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. Solving this equation for 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:- Let’s start with the equation we derived earlier from Kirchhoff's Law… Rearrange and integrate… Solve for i … ( i - )  

8. Series R-L Circuits The time constant:- The time constant is the time at which the power of the “e” function is “-1”. Therefore, time constant is L/R

9. Series R-L Circuits Energy and Power P battery = P resistor + P inductor S 1 S 2 ε L R a b c i

10. References www.humbleisd.net www.gujarat-education.gov.in

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