Suppose you had three boxes, labeled A, B, and C, each having two terminals. We

Question

Suppose you had three boxes, labeled A, B, and C, each having two terminals. We put the arrangement of bulbs in the boxes shown below (a) Rank the networks A, B, and C by their resistances. Which has the most resistance? The least resistance? (b) Rank each of the networks according to the total current through a battery. Explain your reasoning! (c) For each of the circuits 1 through 5 shown above, sketch a standard circuit diagram showing all the bulbs in the circuit. In each diagram number the bulbs and describe which bulbs or combination of bulbs are in series and parallel connections with each other.

Explanation / Answer

a )

suppose each bulb have resistance = R

for

A = R

B = 2R

C = R/2 = 0.5R

B>A>C

part B

i = V / R

so one more R less current so

ic>ia>ib

Part C

let's take all batteey have voltage = V so

in 1

r = R so i = v/R

in 2

series

r= 2R so i = v/2R = 0.5 (v/R)

in 3

parallel

r = 0.5R so i = v/0.5R = 2( v/R)

in 4

A & B are in parallel so total reisitance

1/r = 1/A + 1/B   

1/r = 1/R +1/2R

r = 0.67 R so i = V/ 0.67 R = 1.49 ( v/R)

in 5

A and B in series

so

r = A+B = R +2R = 3R

i = V/ 3R = 0.33( V/R)

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