Hi, can somebody please help me with this inductor problem? I'm stuck on it and need some help i think that I have the general idea, but need some guidance.
This is a step-value function and will need to be solved piece-wise. For t 0 to 5us: Since I (1/L) Vdt therefore:: I (1 / 2E-3) * 10V * 5us 500 * 10V * 5us 25mA For t 5us to 15us I (1 / 2E-3) * -10V * 10us 500 * -10V * 10us -50mA For t 15us to 20us I (1 / 2E-3) * 10V * 5us 500 * -10V * 5us 25mA The total current from t 0 thru t 20us 25mA -50mA +25mA 0 mA
Hello my old friend, I see you're still trying to penetrate basic electrical theory. Let's see if you're correct here: The relevant equation (the origin of which you can check in any circuitry textbook) is; v(t) L.di/dt where v is the voltage applied to the inductor. Therefore; i (1/L).∫v.dt 500 ? ∫v.dt when v is constant this gives i 500 ? v ? t Because of the step-wise shape of your voltage curve, we have to determine the integral in time-steps: From t 0 to 5μs, i 500 ? 10 ? t so it is the line i 5000 ? t, reaching 25mA after 5μs. From t 5 to 15μs, i drops with a gradient of -5000 from its value of 25mA. In this range it is therefore given by the straight line i 0.05 – 5000 ? t. and it reaches a value of -25mA at t 15μs. From t 15 to 20μs the gradient is again +5000 so that the current is given by the equation: i -0.1 + 5000t so that it rises to a value of zero at t 20μs. This is to be expected since the total postive area (integral) under the voltage curve equals the total negative area, so that the overall integral from 0 to 20μs is zero. In conclusion, I don't know whether you're right or wrong because I don't quite follow your thinking. Anyway the above is how it is! I'm afraid I can't get a sketch into Y!A. I hope you're into BA awards in the meantime! Edit: I'm afraid Steven (notwithstanding his HUGE experience) gets it wrong. For example in the second interval 5 to 15μs he calculates the correct change in current but fails to account for the 25mA flowing at the start of that interval. In the third interval he makes (in principle) the same mistake. He also fails to provide any clue about the current waveform as requested in the question!
