Question

B oth 100 Day PH262 Page 1 of 5 Lab #13 AC Circuits, Part 1 RC & RL, Phase Measurements THEORY The rotating phase representation for series AC circuits should be familiar from textbook and lecture notes A brief outline of the essential points is provided here. If a series RLC circuit is connected across a source of om which is a sinusoidal function of time, then und all its derivatives will also be inside. Sonce all demits in a secinct share the same surrent it is customary to write i-Cos ) as the reference function against which the others will be compared. The voltase across each component is then expressed in terms of the current vy-R RICost) - ----LIS -2 fide .Co ) --X, IS ) - Sun ) Sint) - XIS ) V Sine) where lower case symbols are used for time-varying quantities, and upper-case symbols for the amplitudes The ratio of amplitudes V. I is seem to be the DC resistance, R. The bios of the Volamplitudes for the other two components, which must also have units of ohms, are given the symbol X and are called "rectance". leading to the name "reactive components to describe any Lorin a circuit Examination of the rightmost terms in each of these equations shows the relative phase of the the voltage Vit has the same phase asi (both Cos). vc Sin) is 90° behind i, and VLC-Sin) is 90 shead of i. These relationships are frequently expressed by phasor diagrams, which show the voltage amplitudes summed with the appropriate phases to equal the amplitude of the driving em. Figure 1 Above are the voltage phasor diagrams for an RL and an RC circuit. As is conventional, the phasoro Is assumed to be counterclockwise. Thus, it is seen that the external em will be ahead of the current in the inductive circuit, and behind the current in the capacitive circuit. Inspection of these diagrams shows trigonometric functions of the phase angle can be expressed as ratios of the voltages, for example Tan OL-V/VR, or Cosc-VE.

Answer 1

OL R = 1 and C= 9/1 =) RC = 4 x 2 =) RC = 9 a unit of RC = unit of a = As as so mit of RC a unit of the Energy stored in inductor - 1/2 LI? so, unit of L = unit of energy unit of I2 Energy dissipated in resistance = I²Rt so, unit of R = JAS ③ Energy stored in capacitor = av so, unit of C = unit of q² . unit of energy I Now unit of WL = 5x5/A² - J/A-s = wit of Ri unit of toc = 2 x Aghor = T/AS - unit of R - unit of WL = mit of toc = unit of R

derivative of cos(wt+d) = - W sin (wt+ o) = w cost wt + 8 + 7 ) Here phase of derivative is wt+ 6 + 7 and phase of coscot+6) = wt+o which shows that phase of derivative is an advance from the phase of cos(utto let internal resistance of inductor is r - Z +(wej? we know that coso = 2 2) Coso = 2 so, & will decrease from th which is fore pune inductor from the expression it is clear that if w will be low then ang and if will be high zz wh So, this effect will be more important for low frequency.