CJC AC concise notes

Alternating Current An alternating current is the current which direction of flow of charge carriers reverses periodically with time. An example of an alternating current follows the harmonic function of time, as depicted below. We can describe the graph with the following relation: I = I0 sin ωt = I0 sin (2πf)t Note: Although the AC circuit may be different from the DC circuit in some ways, the AC circuit can still be described by the equations that apply to DC circuits. Therefore, we can do the following analysis: Using Ohm’s Law, V = IR = (I0 sin ωt)R = I0R sin ωt = V0 sin ωt Therefore, we get the relation for the alternating potential difference (voltage) with respect to time: V = V0 sin ωt = V0 sin 2πft Graph of current vs time of a sinusoidal AC

Quantifying AC: Root-Mean-Square Values Root-Mean-Square value is the effective value of a continuously varying quantity, obtained from many samples taken at regular intervals during a cycle. The root-mean-square of an alternating current (or voltage) is defined as the value of steady direct current (or voltage) that dissipates energy at the same rate as the alternating current (or voltage) in a given resistance. Iof value meanI=I 2 AC 2 ACrms  Vof value meanV=V 2 AC 2 ACrms  For Sinusoidal AC 2 II 0 rms  2 VV 0 rms  Graphical Derivation of Root-Mean-Square Values of AC The calculation for r.m.s. values can be done graphically. In fact, in most cases, the graphical method is more direct. Here is how the method can be carried out. To find Irms : Step (1) : From the I-versus-t graph, sketch the I2-versus-t graph. Step (2) : From the graph in step 1, deduce the mean value of I2 (in other words, calculate the ratio: T 1 T 1 for graph the under Area ). Step (3) : Calculate the square-root of the mean value of I2 to obtain the Irms. Employ the same method to calculate Vrms starting from the V-versus-t graph.

Relationship between r.m.s. values and Average Power <P> rmsrms oo 000 VI 2 V 2 I = VI2 1=P2 1 =P          rmsrmsVI P  In general for any AC, R V RI VI P 2 rms2 rmsrmsrms  But for sinusoidal AC only, R2 1 2 1 2 1 0 000 V = RI = VI = P 2 2 Rectification Rectification is the means by which alternating current is converted into direct current. Diodes are used to achieve half-wave or full-wave rectification. A simple single diode set up for half-wave rectification