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lecture12 - 12 Lecture 12 12.1 LR circuit comparison with...

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12. Lecture 12 12.1 LR circuit, comparison with RC An inductor stores energy in the form of a magnetic field similarly as a capacitor stores energy in the form of an electric field. In both cases we can ”charge” the device by loading energy into it taking it it for example from a battery. In the case of a capacitor we did that through a resistor in an RC circuit. The charging time is given by τ = RC . See the fig.68 to remind yourself how the current and voltage behave as a function of time in such case. ± ² ± ² ± ³ ³ ´ µ¶ Figure 68: AS seen before, energy from a battery can be stored in a capacitor using an RC circuit. The time constant of the circuit is given by τ = RC . Compare with the RL circuit below. We can do the same for an inductor by using an RL circuit, a resistor in series with an inductor. See fig.69. Initially, when we turn on the switch, the battery tries to increase the current in the circuit and that will occur almost instantaneously if the inductor is replaced by a cable. However such large changes in current are opposed by the inductor which creates between its terminals a voltage that opposes the increase in current. For that reason the current increases at a slow rate until it reaches its final value given by: I f = 1 R V battery (12.1) at that time the current does no change anymore and the inductor behaves as a cable, namely no voltage cross it terminals. However the inductor is generating a magnetic field so it has energy stored in it. To see how long it takes to reach such a stationary state, consider the voltage across the inductor V a V b = L I t (12.2) – 80 –
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Initially, as we said, the inductor opposes the battery and does not allow any current to circulate. This means that V a V b = V battery and the initial slope with which the current start increasing is then: I t = 1 L V battery (12.3) As the current increases, this slope decreases as can be see in the plot in fig.69. However, we get a good estimate of the time it takes to reach the steady state if we assume the slope to be constant and ask how long it would take with that slope to reach the current I f . It is t = I f I t = V battery R 1 V battery L = L R (12.4)
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