How did he integrate this step?

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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ENG
How did he integrate this
step?
Example 2.2: Finding the Performance Parameters of a Battery Charger
The battery voltage in Figure 2.4(a) is E 12 V and its capacity is 100 Wh. The
average charging current should be Ide = 5 A. The primary input voltage is Vp =
120 V, 60 Hz, and the transformer has a turn ratio of n = 2:1. Calculate
(a) the conduction angle & of the diode.
(b) the current-limiting resistance R.
(c) the power rating PR of R.
(d) the charging time ho in hours.
(e) the rectifier efficiency n.
(f) the PIV of the diode.
Solution of Example 2.2
E = 12 V, V, = 120 V, V, = V/n= 120/2 = 60 V, and Vm= V2 x Vs, = v2 x 60 =
84.85 V.
a) From Eq. (2.17), a = sin (12/84.85) = 8.13° or 0.1419 rad. B 180 8.13 =
171.87°. The conduction angle is 8 = B- a = 171.87-8.13 = 163.74°.
b) The average charging current Ide is.
sin ot – E
(2V cos a +2Ea- nE), for B = n- a
2R
2л
R
(2.18)
which gives
1
(2V cos a + 2Ea- nE)
2d de
R =
1
(2x84.85x cos 8.13 +2x12x 0.1419 - nx12)= 4.262
2n x5
c) The rms battery current Ims is
1", sin ox – E) d(ox)
%3D
27
a
R²
V2
sin 2a - 4V E cos a
1
+E (7-2a)+.
(2.19)
2 7R?
I = 67.4
I = 8.2 A
The power rating of R is PR = 8.22 x 4.26 = 286.4 W.
ING
CAL ENG
Transcribed Image Text:ENG How did he integrate this step? Example 2.2: Finding the Performance Parameters of a Battery Charger The battery voltage in Figure 2.4(a) is E 12 V and its capacity is 100 Wh. The average charging current should be Ide = 5 A. The primary input voltage is Vp = 120 V, 60 Hz, and the transformer has a turn ratio of n = 2:1. Calculate (a) the conduction angle & of the diode. (b) the current-limiting resistance R. (c) the power rating PR of R. (d) the charging time ho in hours. (e) the rectifier efficiency n. (f) the PIV of the diode. Solution of Example 2.2 E = 12 V, V, = 120 V, V, = V/n= 120/2 = 60 V, and Vm= V2 x Vs, = v2 x 60 = 84.85 V. a) From Eq. (2.17), a = sin (12/84.85) = 8.13° or 0.1419 rad. B 180 8.13 = 171.87°. The conduction angle is 8 = B- a = 171.87-8.13 = 163.74°. b) The average charging current Ide is. sin ot – E (2V cos a +2Ea- nE), for B = n- a 2R 2л R (2.18) which gives 1 (2V cos a + 2Ea- nE) 2d de R = 1 (2x84.85x cos 8.13 +2x12x 0.1419 - nx12)= 4.262 2n x5 c) The rms battery current Ims is 1", sin ox – E) d(ox) %3D 27 a R² V2 sin 2a - 4V E cos a 1 +E (7-2a)+. (2.19) 2 7R? I = 67.4 I = 8.2 A The power rating of R is PR = 8.22 x 4.26 = 286.4 W. ING CAL ENG
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