27 10. Square Resistor Networks Suppose four identical resistors R are connected

Question

27 10. Square Resistor Networks Suppose four identical resistors R are connected in a square array In one case (A), external leads are attached at opposite corners, and in one case (B), external leads are attached on a single side. (a) Find the equivalent resistance of the network in both cases. (b) Suppose the external leads are connected to a power supply with voltage V. Find the total power dissipation in both cases (c) Label the individual resistors and find the power dissipation in each resistor in both cases. Verify that the individual power values add up to the total power dissipation.

Explanation / Answer

a)Let each resistance be R

in first one the 2Rs are in eries and their combination is in parallel

1/Req = 1/2R + 1/2R

RA = R

Now in second, three Rs are in series and their combination is in parallel to one R

1/Req = 1/3R + 1/R

1/RB = 4/3R

RB = 3/4 R

b)I1 = V1/R

P = V1I = V1^2/R

Hence, P = V^2/R

I2 = V2 (4/3R)

P2 = V2 x V2 4/3R = 4 V^2/3R

P = 4V^2/3R

c)I' = V1/2R

drop is V1/2

Power for all

P = VI = V1^2/4R

P = V^2/4R

P = V^2/R

for songle resistor,

P = V^2/R

for the others, voltage drop is V/3

P = V^2/R = V^2/9R

since the resistance is same, they will have the same drop and power disspiation across them.

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