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 R_1 = 25.0 ohm and R_2 = 86.0 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. 13.3 (b) Find the current delivered by the battery to this equivalent resistance. 0.9 (c) Determine the power delivered by the battery. 10.8 (d) Determine the power delivered to the 50.0 ohm resistor. 1.92

Explanation / Answer

step;`1

Given that

resistance R1=25 ohm

resistance R2=86 ohms

now we find the equivlent resistance

resistance R1 and 50 ohms series connection

resistance R'=50+25=75 ohms

resistance R' and R2 are parallel connection

resistance R"=75*86/75+86=6450/161=40.1 ohm

the resistance R" and 20 ohms are series connection

the equivalent resistance Req=40.1+20=60.1 ohm

step;3

now we find the current delivered in the equivalent resistance

current I=12/60.1=0.2 A

step;4

now we find the power delivered by the battery

power P=iV=0.2*12=2.4 W

step;5

now we find the power delivered to the 50 ohms resistance

the current in the 50 ohms resistance =75*0.2/75+86

                                                        =15/161

                                                         =0.1 A

the power in the 50 ohms resistance P2=0.1^2/50=0.0002 W

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