PROBLEM # 7.17
The 240 V, 2 Ω source in the circuit shown is inadvertently short-circuited at its
terminals a – b. At the time the fault occurs, the circuit has been in operaton for
a long time.
a) What is the initial value of the current iab in the short-circuit connection
between terminals a – b?
Just before the short circuit occurs, the circuit looks like
IT
I1
IT 
240
240

 30 A
2  10 15
8
15
 18 A
25
10
I 2  30  12 A
25
I1  30
I2
At t = 0+, the circuit looks like
IT
iab
18A
12A
240
 120 A
2
iab  IT  I1  I 2  120  18  12
IT 
iab  90 A, t  0 
b) What is the final value of the current iab?
The circuit at t = ∞
iab
iab () 
240
 120 A
2
c) How many microseconds after the short circuit has occurred is the current in
the short equal to 114A?
The circuit for t > 0+
120A
iab
i1
18A
i2
12A
i1 (0)  18 A
2 103
1 
 0.2ms
10
1
 5000
1
i2 (0)  12 A
6 103
2 
 0.4ms
15
1
 2500
2
i1 ()  i2 ()  0
i1 (t )  18e 5000t A, t  0
i2 (t )  12e 2500t A, t  0
iab  120  18e 5000t  12e 2500 t
114  120  18e 5000t1  12e 2500t1
6  18e 5000t1  12e 2500t1
x  e 2500t1
6  18 x 2  12 x
1  3x 2  2 x
3x 2  2 x  1  0
x  1, x 
1
3
1
 e 2500t1
3
1
ln  2500t1
3
1.09  2500t1
t1 
1.09
 439  s
2500