Thursday, Apirl 22, 1999

Announcements:
1. AC and RLC Circuits will be covered on April 22 and 27
2. Suggested HW problems that will not be collected : Chapter 33: 47, 51, 53, 65, 85, 87
The answers will be posted on April 29
3. Maxwell's equations will be covered in lecture on April 29. Expect 1 to 2 qualitative questions on the final
4.Recitation Instructors will annouce "normilazation" policy for  recitation grade.
5. "Normilazation" of lab grade will be announced next Tuesday.
6. More information on final will be announced in Tuesday and Thursday's lecture.

Lecture notes:
Capacitive Load

• x = x_max sin wt    v_c = V_c sin wt
• q_c = cv_c = cV_csin wt
• i_c = dq_c/dt = w cV_ccos wt
• See Figure 33-9b
• Note that cosq = sin (q +90)
• Therefore: i_c = w cV_ccos wt = w cV_csin (wt + 90^o)
•   v_c = V_c sin wt
• Therefore, i_c leads v_c by 90^o or p/2 radians. They are out of phase by 90^o .
• See the phasor diagram in the text (Figure 33-9c
• For a capacitive load: i_c  = w cV_csin (wt + 90^o) =  = V_csin (wt + 90^o)/ X_c
• X_c = 1/ w c = Capacitive reactance

• See Figure 33-10a for a picture
• v_L = V_L sin wt = L di_L/dt ;   di_L/dt = v_L/L = V_L/L sin wt
• Therefore, i_L = I(Integral) di_L = V_L/L I(Integral) sin wt dt = - (V_L/wL) cos wt
• X_L = wL = inductive reactance
• Note that   -cos wt = sin (wt -90)
• Therefore, i_L = -(V_L/wL) cos wt = (V_L/wL)sin (wt -90) = I_Lsin (wt -90)
• When   v_L = V_L sin wt, therefore i_L and v_L are 90^o out of phase but i_L  lags behind
• See Figure 33-10b and 33-10c

• For resistor,  i_R and v_R are in phase.Therefore if v_R = V_Rsin wt  and i_R = I_Rsin wt, then i_R =V_R/R sin wt.
• For a capacitor, i_c leads v_c by 90^o. If v_c = V_c sin wt, then  i_c  = I_csin (wt + 90^o) =  i_c  = V_c/X_csin (wt + 90^o) where X_c = 1/wC.
• For an inductor,  i_L and v_L are 90^o out of phase but i_L  lags behind. If v_L = V_L sin wt, then i_L = I_Lsin (wt -90) = V_L/X_Lsin (wt -90) where X_L = wL.

• An emf of x =x_max sin wt is applied. Since R, L, C are in series, the same current is flowing in the circuit.  i = I sin (wt-j)  where j  is the phase angle  or phase constant; because of L and C, we do not expect the phase constant to be equal to zero.