Chapter 10 transcend response capacitors and inductors. Let's explore the response of capacitors and inductors. A little further, a sudden change in DC voltage is called a transient voltage. As we have seen, unlike resistors, which respond instantaneously to the applied voltage, capacitors and inductors react over time as the absorb and or release energy. In an RC series circuit as shown here, when the switch is first closed, the voltage across the capacitor, which we were told was fully discharged at the beginning is zero volts. Thus, it first behaves as though it were a short circuit over time that capacitor voltage will rise to equal the battery voltage ending in a condition where the capacitor now behaves as an open circuit as the capacitor voltage of approaches the battery voltage the current approaches zero.

However, the time required for a charge in voltage of 63% of the supply voltage is given by what is known as the time constant, which is equal to RC, the resistance and the capacitance. Sometimes they let that time constant equal to a Greek letter tau, but we'll just let it equal t for now and call it the time constant. In this case, t is equal to RC. And given the quantities of one kale and one microfarad, it equals one millisecond. The capacitor voltages approach to the battery voltage and the current approach to zero over time. They both approach their final values getting closer and closer over time but they never exactly reached their final destination.

For all practical purposes, though, we can say that the capacitor voltage will eventually reach the battery voltage, and that the current will eventually reach zero after a time period of five time constants. When the source is removed from the circuit, and the capacitor is short circuited through a resistor, the capacitor voltage drops and approaches zero volts, and the current also approaches zero over time. As the electric charge dissipates. They both approach their final values getting closer and closer over time, but again, never exactly reaching their destination. For all practical purposes, though, we can say that a capacitor voltage will eventually reach zero after a time period of five times constants. However, the time required for a drop in voltage of 63% is given by the time constant RC.

In this case, t is equal to RC is equal to one times 10 to the three times one times 10 to the minus six which equals one millisecond. In describing the transient response of capacitor, it can be defined in terms of its time constant, t is equal to RC, where t is time in seconds, C is the capacitance in ferrets, and r is the resistance in ohms. The time required for a change in voltage of 60 63% is one time constant. It is accepted that a capacitor voltage reaches its steady state value after five time constants. In an RL series circuit as shown here, when the switches first closed, the voltage across the inductor will immediately jump to the battery voltage acting as the were an open circuit, and then decay down to zero over time, eventually acting as though it were a short circuit. When the switches first closed, the current is zero, then it increases over time until it is equal to the battery voltage divided by the series resistance in this case, one kale or 1000 ohms.

This behavior is precisely opposite to that of the series resistor capacitor circuit, where current started at a maximum And capacitor voltage was at zero. Just as with the RC circuit, the inductor voltage approaches zero, and the current approaches to 10 milliamps over time. For all practical purposes, though, we can say that the inductor voltage will eventually reach zero volts, and the current will eventually equal a maximum of 10 milliamps. However, the time required for the current to read 63% is given by the time constant L divided by R or the inductance divided by the resistance. In this case, the time constant T is equal to L divided by r, which is equal to one divided by 1000 or it's equal to one millisecond. inductors have the opposite characteristic of capacitors where capacitors store energy and electric field produced by the voltage between two plates inductors store energy in a magnetic field produced by the current through the wire.

Once the inductors terminal voltage has decreased to a minimum, zero for a perfect inductor, the current will stay at a maximum level and the inductor will behave essentially as a short circuit. The transient response of an inductor can be described by its time constant tau or t which is equal to L divided by r, where t is in seconds L is in Henry's and r is in ohms. The time t required for a change in current of 63% is one time constant. inductor current reaches its steady state value in fact, time constants for both capacitors and inductors, their plots are similar and follow what is referred to as the universal time constant graphs where they're rising curve values increased 63% each time constant and can be rep and can represent capacitors charging voltage VC or the rising inductor current i L. The falling curves values decrease 63% with each time constant, the time required for a drop in voltage of 63% and can be raised and can represent capacitor discharging voltage or it can also refer to decaying inductor current This is the universal rising curve in percent plotted against time in time constants.

After one time constant the value has increased to 63%. This curve can either represent the capacitor charging voltage or inductor rising current. This is the universal falling curve in percent plotted against time. In time constants. After one time constant, the value has experienced a drop of 63%. After one time constant, this curve can either represent the discharge in the capacitor discharge in volts or The decaying inductor current, you will notice that the curve was generated by the Formula E to the negative tau times 100%, which falls from 100% to zero percent shown in red.

The percent drops shown in blue measures how much the curve has dropped from zero percent to 100%. By measuring this quantity, we only have to remember a one fact for both the rise and falling curves and that is the 63 63% after one time constant. This ends chapter 10