http://www.webassign.net/ncsuplseem2/4-post-06.gif (picture of circuit) (a) S 1

Question

http://www.webassign.net/ncsuplseem2/4-post-06.gif  (picture of circuit)

(a) S1 and S2 are closed while S3 is open. What is the current through each bulb?

(b) S3 is closed while S1 and S2 are open. What is the current through each bulb?

(c) S2 and S3 are closed while S1 is open. What is the current through each bulb?

(d) S1 and S3 are closed while S2 is open. What is the current through each bulb?

(e) All three switches are closed. What is the current through each bulb?

bulb 1      bulb 2      bulb 3      bulb 4      S1 and S2 are closed while S3 is open. What is the current through each bulb? S3 is closed while S1 and S2 are open. What is the current through each bulb? S2 and S3 are closed while S1 is open. What is the current through each bulb? S1 and S3 are closed while S2 is open. What is the current through each bulb? All three switches are closed. What is the current through each bulb?

Explanation / Answer

(a) In this case, there is a short circuit from Bulb 1 to Bulb 2, so R-equiv is 170 ohms,

and the current through each of Bulbs 1 and 2 is 0.235 amps. No current through 3 and 4.

(b) In this case, Bulbs 1,3,4 are in series, R-equiv is 255 ohms; current through 1,3,4

is 0.157 amps. No current through Bulb 2.

(c) In this case, Bulbs 1 and 3 are in series with the parallel-resistance combination

of Bulbs 2 and 4. R-equiv for the whole circuit is 2.5 x (85 ohms), and the current

through Bulbs 1 and 3 is 0.188 amps; current is split through Bulbs 2 and 4, 0.094 amps each.

(d) In this case, Bulb 1 is in series with a parallel combination whose two branches are

(i) Bulb 2 and (ii) Bulbs 3 and 4 in series. R-equiv for the whole circuit is

85 + 1/(1/85+1/170) = 141.67 ohms.

Current through Bulb 1 is 40 V / 141.67 ohms = 0.282 amps.

The parallel branches split this current, with twice as much of it going through Bulb 2

as through the 3-4 series combo. So the current in Bulb 2 is 0.188 amps, and the

current through Bulbs 3 and 4 is 0.094 amps.

(e) I'm less certain of this one, but I think no current will go through Bulb 3,

because the only place you can go from there is to Bulb 2 or Bulb 4, both of

which can be reached from Bulb 1 with (theoretically) no resistance at all.

Of course, in a real circuit, the wires have SOME resistance, but not much.

So I think this one is going to behave as if the parallel combination of Bulb 2 and 4

is in series with Bulb 1. Hence, R-equiv is 1.5 x 85 ohms = 127.5 ohms.

Current through Bulb 1 is 0.314 ohms, currents through Bulbs 2 and 4 are 0.157 each.

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