Consider the three resistors R_1 = 17ohm, R_2 = 27ohm, and R_3 = 89ohm in the co

Question

Consider the three resistors R_1 = 17ohm, R_2 = 27ohm, and R_3 = 89ohm in the configuration shown in the figure. A potential difference deltaV = 7.5V is applied between A and B. Express the equivalent resistance R_e of the combination of R_2 and R_3 in terms of R_2 and R_3. Express the total resistance R off tire combination of all three resistors in terms of R_1, R_2 and R_3. Calculate the numerical value of the total resistance R in ohm. Express the current I on R_1 in terms of the potential difference deltaV between A and B and the equivalent resistance R. Calculate the numerical value of I in A. Express the voltage across R_2, deltaV_2, in terms of deltaV, I, and R_1. Express the current I_2 through R_2 in terms of deltaV_2 and R_2. Calculate the numerical value of I_2 in A. Calculate the numerical value of I_3 through R_3.

Explanation / Answer

R2 AND R3 ARE IN PARALLEL

so there equivent = R2R3 / (R2+R3)

R1 is in series with this equivalent

Re = R1 + R2R3/(R2+R3) = R1R2 + R1R3 +R2R3 / R2 + R3

Re = 17*27 + 17*89 + 27*89 / (27+89)

Re = 37.71 ohm

d) V= IR

I = V/R = 7.5/37.71 = 0.1988 A

f)volateg across R2 = I*R = 0.1988*20.71 = 4.12 V

current though R2 = 0.1988*89 / (27+89) = 0.1525A

current through R3 = 0.1988*27 / (27+89) = 0.04627 A

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