RC and RL
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RC AND RL TRANSIENT RESPONSES Capacitors oppose changes in voltage. Inductors oppose changes in current. The time constant in a capacitor circuit is the product of the resistance and capacitance. T = RC. The time constant of an inductor circuit is the inductance divided by the resistance. T = L/R. A time constant is the time needed for a change of 63.2 % in the voltage across a capacitor or the current through the inductor. Time constants allow for the examination of transient reponses in series RC and RL circuits. A transient response is a temporary condition involving a changing voltage or current that exists only until a steadystate value of either voltage or current is reached. Transient responses are associated with nonsinusoidal voltage and current waveforms (for example, square, rectangular, and triangular) and with a DC source being switched on and off. The effects of inductance and capacitance on nonsinusoidal waveforms is to produce a waveshape change. RC and RL circuits are used to provide filtering, waveshaping, and timing. The capacitor is most commonly used. Capacitors are smaller and more economical than inductors and do not of strong magnetic fields. RC CHARGE AND DISCHAGE CYCLES Charge Cycle An RC series circuit contains a voltage source with a resistor and a capacitor in series. A switch provides the charge or discharge. t0 is the time when the switch is first closed. t1 is the time when the capacitor reaches full charge or discharge. The time to fully charge or discharge the capacitor is equal to five time constants. The source voltage instantly rises from zero to maximum and stays at this value. The circuit current instantly rises to maximum and then gradually decreases as the capacitor charges. When the capacitor is fully charged the current at zero and remains zero. The voltage across the resistor instantly rises to maximum and then gradually drops. The voltage across the capacitor gradually increases to maximum. Discharge Cycle When the switch is moved to the discharge position the source voltage instantly drops to zero. The discharge current instantly goes to maximum and then gradually decreases. The resistor voltage instantly goes to maximum. The voltage gradually decreases to zero. The capacitor voltage also decreases gradually until it reaches zero. High Capacitive Discharge Current The circuit can be configured to provide a high discharge current for an instant in time. This is commonly used for flash photography. RC TIME CONSTANT The time required to charge a capacitor to 63.2 % or discharge to 36.8 % of the maximum voltage is a time constant. T = RC R is in ohms C is in Farads. After five time constants the voltage is 99.3 % which is generally considered fully charged. Mohm x uF = s Kohm x uF = ms Mohm x pF = us UNIVERSAL TIME CONSTANT CHART The chart may be used to find the voltage or current value for any amount of time. RC EXPONENTIAL EQUATIONS CapacitorCharging EquationsCapacitor Voltage Capacitor Current Charging Voltage Time CapacitorDischarging EquationsCapacitor Voltage Capacitor Current Discharging Voltage Time L/R TIME CONSTANT t = L / R High Voltage Produced when an RL Circuit Is Opened When a circuit is opened the magnetic field of an inductor collapses. The collapsing magnetic field will induce a high voltage. Diodes are often used in inductor circuits such as relays to prevent this high voltage from causing damage to circuit components. L / R EXPONENTIAL EQUATIONS Inductor Current Equation Inductor Voltage Equation LONG, MEDIUM, AND SHORT TIME CONSTANTS RC circuits are used more frequently than RL circuits. Long Time Constant Medium Time Constant Short Time Constant RC INTEGRATOR RC DIFFERENTIATOR 