By S. A. Knight (Auth.)
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Extra info for Electrical and Electronic Principles. Volume 3
Sample text
Cos φ = apparent power Hence = cos 0 VI true power = apparent power x power factor If the impedance of the circuit is Z, then COS 0 = R R 2 Z resistance 2 V(R +X ) impedance These statements are true only for sinusoidal waveforms. cos φ but 0 is not in general the angle of phase difference between current and voltage. (11) Show that true power can be expressed in the alternative forms I2Zcosφ and (V2/Z)cosφ Follow the next example carefully. It illustrates two methods of calculating circuit power.
Component of voltage and a purely alternating component of voltage, and only the alternating component appears across R. In many circuit applications it is necessary to re-insert the steady component if the output has to be taken from R. c. restoration. C. transients Example (19). 23(b). Sketch the output wave form, marking the high and low voltage levels attained and indicating the new zero level. 001 s or 1000 ßs, which is long compared with the period between the pulses, 50 MS. Taking the output from across the resistor where the shape of the input waveform will be practically unaffected, the average value of the input is clearly Pmean = mean P Px+P2 10 .
However, if C is ex pressed in μ¥, the time will be given in μ$. It is often easiest to work in μ¥ for C and ΜΩ for R, the answer then again being given in seconds. Example (5). What is the time constant of a 4 μ¥ capacitor and a 100 kΩ resistor? Work the problem first in farads and ohms, and then in μ¥ and ΜΩ. 4 s Alternately, working in μ¥ and ΜΩ T= 4 x 0 . 4 s Example (6). A 10 μ¥ capacitor and a 2 ΜΩ resistor are swit ched suddenly to a 100 V supply. Find (a) the time constant, (b) the initial current, (c) the initial rate of rise of voltage across C.