(c27p74)The figure shows a circuit containing three switches, labelled S1, S2, a
ID: 3161392 • Letter: #
Question
(c27p74)The figure shows a circuit containing three switches, labelled S1, S2, and S3. Find the current at "a" for all possible combination of switch settings. Put e = BO v, RI = 15 omega and R2 = 10 omega. Assume that at the battery has no resistance. Current at "a" for S1 and S2 and S3 open Current at "a" for S1 closed and S2 and S3 open Current at "a" for S1 and S2 closed S3 open Current at "a" for S1 and S2 and S3 closed Current at "a" for S1 and S3 closed and S2 open Current at "a" for S3 closed and S1 and S2 openExplanation / Answer
Here, when all S1 , S2 , S3 are all open ,
as the circuit is not complete ,
the current at a is ZERO
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when S1 is closed
for the equivalent resitance
Req = 2 * R1 = 2 * 15 = 30 Ohm
current at a = E/Req
current at a = 80/30 A
current at a = 2.67 A
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when S1 and S2 is closed
when S1 is closed
for the equivalent resitance
Req = 1/(1/(R1 + R2) + 1/R1) + R1
Req = (1/(15 + 10) + 1/15) + 15
Req = 15.1 Ohm
current at a = E/Req
current at a = 80/15.1 A
current at a = 5.30 A
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when all S1 , S2 , S3 are all closed
for the equivalent resitance
R3 = R1 + R2 = 10 + 15 = 25
R4 = 25 * 15/(15 + 25) = 9.4 Ohm
R5 = 9.4 + 10 = 19.4 Ohm
R6 = 19.4 * 15/(19.4 + 15)
R6 = 8.46 Ohm
Req = 8.46 + 15 = 23.46 Ohm
current at a = E/Req
current at a = 80/23.46 A
current at a = 3.41 A
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please post rest in a seperate question
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