Three Switches Figure 27-24 shows a circuit containing three switches, labeled S

Question

Three Switches Figure 27-24 shows a circuit containing three switches, labeled S1, S2, and S3. Find the current at a for all possible combinations of switch settings. Put '8-100 V, R1-25.0 ?, and R2-10.0 ?. Assume that the battery has no resistance. Ri Ri Ri Figure 27-24 S?, S2, and S3 all open S1 closed, S2 and S3 open S2 closed, S? and S3 opern S3 closed, S1 and S2 open S1 open, S2 and S3 closed S2 open, S1 and S3 closed S3 open, S1 and S2 closed S1, S2, and S3 all closed Section 27.4 Multiloop Circuits Section 27.5 Parallel Resistance

Explanation / Answer

when S1,S2 and S3 all open .......current at a = 0 A

When S1 closed ,S2 and S3 open...current at a is i = e/(R1+R1) = 100/(25+25) = 2 A

when S2 closed,S1 and S3 open,,,,i = e/(R1+R2) = 100/(25+10) = 2.86 A

when S3 closed,S1 and S2 open ......i = e/(R1+R2) = 100/(25+10) = 2.86 A

When S1 open,S2 and S3 closed....i = e/((R1+R2)*R1/(R1+R2+R1)) = 100/((25+10)*25/(25+10+25)) = 6.86 A

when S2 open ,S1 and S3 closed ...i =

Net resistance of the circuit is Rnet

[(R1+2R2)*R1/(R1+2R2+R1)] + R1 = ((25+20)*25/(25+20+25)) + 25 = 41.07 A

i = 100/41.07 = 2.44 A

When S3 open ,S1 and S2 closed ....i =

Rnet = ((R1+R2)*R1/(R1+R2+R1)) + R1 = ((25+10)*25/(25+10+25))+25 = 39.6 A

i = 100/39.6= 2.53 A

when S1,S2 and S3 all closed

i = e/Rnet

Rx = (R1+R2)*R1/(R1+R2+R1) = (25+10)*25/(25+10+25) = 14.58 ohm

Ry = 14.58+ R2 = 14.58+10 = 24.58 ohm

Rz = 24.58*25/(24.58+25) = 12.4 ohm

Rnet = 12.4+25 = 37.4 ohm

i = 100/37.4 = 2.67 A

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