In the circuit shown below the 4 bulbs are identical and have a resistance of 85

Question

In the circuit shown below the 4 bulbs are identical and have a resistance of 85 each. The battery supplies a voltage of 40 V. S1, S2, and S3 represent switches.

http://www.webassign.net/ncsuplseem2/4-post-06.gif

(a) S1 and S2 are closed while S3 is open. What is the current through each bulb?
bulb 1        
bulb 2        
bulb 3        
bulb 4        

(b) S3 is closed while S1 and S2 are open. What is the current through each bulb?
bulb 1        
bulb 2        
bulb 3        
bulb 4        

(c) S2 and S3 are closed while S1 is open. What is the current through each bulb?
bulb 1        
bulb 2        
bulb 3        
bulb 4        

(d) S1 and S3 are closed while S2 is open. What is the current through each bulb?
bulb 1        
bulb 2        
bulb 3        
bulb 4        

(e) All three switches are closed. What is the current through each bulb?
bulb 1        
bulb 2        
bulb 3        
bulb 4        

Explanation / Answer

(a)

there is a short circuit from Bulb 1 to Bulb 2,

Requ = R1 +R2 = 85+85 = 170 ohms,

current through each of Bulbs 1 and 2 is

V =IR

I = 40/170 = 0.235 amps.

No current through 3 and 4.

(b)

Bulbs 1,3,4 are in series,

Requ = 85+85+85 = 255 ohms

current through 1,3,4 is

I = 40/255 = 0.1568 amps.

No current through Bulb 2.

(c)

Bulbs 1 and 3 are in series with the parallel-resistance combination of Bulbs 2 and 4.

Requ = 2.5 * 85 = 212.5

current through Bulbs 1 and 3 is

I = 40/212.5 = 0.188 amps

current through Bulbs 2 and 4, 0.094 amps each.

(d)

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

I = 40 / 141.67 = 0.282 amps.

current in Bulb 2 is I = 0.188 amps,

current through Bulbs 3 and 4 is I = 0.094 amps.

(e)

no current will go through Bulb 3,

Requ = 1.5 x 85 ohms = 127.5 ohms.
Current through Bulb 1 is I = 0.3137 amp,

currents through Bulbs 2 and 4 are I = 0.157 amp each

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