Figure P26.67 employs a convention often used in circuit diagrams. The battery (
ID: 1555139 • Letter: F
Question
Figure P26.67 employs a convention often used in circuit diagrams. The battery (or other power supply) is not shown explicitly. It is understood that the point at the top, labeled "36.0 V, " is connected to the positive terminal of a 36.0-V battery having negligible internal resistance, and that the ground symbol at the bottom is connected to the negative terminal of the battery. The circuit is completed through the battery, even though it is not shown. (a) What is the potential difference V_ab, the potential of point a relative to point b, when the switch S is open? (b) What is the current through S when it is closed? (c) What is the equivalent resistance when S is closed?Explanation / Answer
(a) WHEN SWITCH S IS OPEN
current = 4A
36 - Va = (6)(4)
=> Va = 12 V
36 - Vb = (3)(4)
=> Vb= 24 V
Vab = Va - Vb = -12 V
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(b) WHEN S IS CLOSED
Using STAR-DELTA tranformation,
Req = {(3+(3/2))II(6+(3/4))} + (3/2) = {(9/2)II(27/4)} + (3/2)
=>Req = 21/5 ohms
Ieq = 36/(21/5) = 60/7 A
Current through 6 ohm resistor = (60/7)(9/2))/[(9/2)+(27/4)] = 24/7
Current through 3 ohm resistor = (60/7)(27/4))/[(9/2)+(27/4)] = 36/7
36 - (24/7)(6) = Va
=> Va = 108/7 V
36 - (36/7)(3) = Vb
=> Vb = 144/7 V
Vab = Va - Vb = 36/7 V
Iab = Vab/3 = 12/7 A
Current through S = 12/7 A
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