Four resistors are connected to a battery with a terminal voltage of 12 V, as sh

Question

Four resistors are connected to a battery with a terminal voltage of 12 V, as shown in the figure below. (Assume R1 = 40.0 ohm and R2 = 83.0 ohm.) (a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit. omh (b) Find the current delivered by the battery to this equivalent resistance. A (C) Determine the power delivered by the battery. W (d) Determine the power delivered to the 50.0-ohm resistor. W

Explanation / Answer

a)

R1=40 ohms  and 50 ohms are in series

R' =40+50 =90 ohms

R'=90 ohms and R2=83 ohms are in parallel

1/R" =1/90 + 1/83

R"=43.18 ohms

R"=43.18 ohms and 20 ohms are in series ,so equivalent resistance

Req=20+43.18=63.18 ohms

Req=63.2 ohms

b)

Current delivered to the battery is

I=V/Req =12/63.2

I=0.19 A

c)

Power delivered by the battery

P=VI =12*0.19

P=2.28 Watts

d)

Current flowing through 50 ohms is

I50=I*(83/83+90) =0.19*(83/173)

I50=0.091 A

Power delivered to 50 ohms is

P50=I502R =0.0912*50

P50=0.415 Watts

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