(i.e., time constant)? It takes time for an RC circuit (or an RL circuit) to reach a steady-state value. This time, we find, is a function of the product of R and C. Actually, if we multiply the value of R in ohms by the value of C in farads, it is equal to time in seconds. In a series RC circuit as illustrated in Figure A.15, the product RC is known as the time constant of the circuit. By definition, it is the time required to charge the capacitor to 63% of its final voltage. If we plot the curve for voltage (E) in Figure A.16, we have an exponential function of time. This is expressed mathematically as Ei=Emax[1 = - e-t/RC], (A.25) Figure A.15 An RC circuit. Max. value Figure A.16 Current and voltage values as a function of time for an RC circuit. A.8 ALTERNATING CURRENTS where E is the instantaneous voltage across the capacitor at any time t, Emax is the final voltage, and E is the natural number. This is the base of the natural logarithm or the Nape- rian logarithm. 6 Its value is 2.718+. When t equals RC, the term in parentheses equals 1-e-1=1-1/e=1-2.718 = 0.63. It should be noted that a similar relationship can be written for an RL circuit where the exponential buildup curve is current rather than voltage. However, here the exponent is L/R rather than RC. Again, it is the time required for the current to build up to 63% of its final value. RC circuits have wide application in the telecommunications field. Because of the precision with which resistors, capacitors, and inductors may be built, they enable the circuit designer to readily control the timing of current pulses to better than 1-msec accuracy. For such practical applications, the designer considers that currents and voltages in RC and RL circuits reach their final value in a time equal to five times their time constant [i.e., 5 X RC or 5 X (L/R)]. It can be shown that at 5 X time constant the current or voltage has reached 99.3 + % of its final value. A.8 ALTERNATING CURRENTS Alternating current (ac) is a current where the source emf is alternating