13 points SerPSE9 28 P016 Four resistors are connected to a battery as shown in

Question

13 points SerPSE9 28 P016 Four resistors are connected to a battery as shown in the figure below Rs-4R (a) Determine the potential difference across each resistor in terms of (use the following as necessary: 8 for .) (b) Determine the current in each resistor in terms of i (c) If R3 is increased, explain what happens to the current in each of the resistors. This answer has not been graded yet (d) In the limit that R3 on, what are the new values of the current in each resistor In terrns of the original onet the battery Need Help?

Explanation / Answer

given 4 resistors in the diagram

a. Reff = R + R4*(R2 + R3)/(R4 + R3 + R2)

R1 = R

R2 = 2 R

R3 = 4 R

R4 = 3R

hecne

Reff = R + 3*6R/9 = R + 2R = 3R

hence current from battery = I

V = I*3R

I = V/3R

so potential difference across R1, dV1 = V/3

potential diff across R4 dV4 = 2V/3

current through R2 = i

2V/3 = i(6R)

i = 2V/18R = V/9R

so dV2 = i*R2 = 2V/9

dV3 = 2V/3 - 2V/9 = 4V/9

b I1 = I

I2 = 2V/9*2R = V/9R = I/3

I3 = I/3

I4 = 2I/3

c. whern R3 is increased, Reff increases

hence

I decreases overall

but

I in R4 would increase overall

otherwise currnet decreases in all resistors

d. R3 -> inf

then

I1 = I4 = V/4R

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