Consider the circuit shown in the figure ( Figure 1 ) . Suppose the four resisto

Question

Consider the circuit shown in the figure(Figure 1) . Suppose the four resistors in this circuit have the values R1 = 13? , R2 = 6.3? , R3 = 6.1? , and R4 = 11? , and that the emf of the battery is E = 18V .

Part A

Part B

Consider the circuit shown in the figure(Figure 1) . Suppose the four resistors in this circuit have the values R1 = 13? , R2 = 6.3? , R3 = 6.1? , and R4 = 11? , and that the emf of the battery is E = 18V . Find the current through each resistor using the rules for series and parallel resistors. Express your answers using two significant figures separated by commas. Find the current through each resistor using Kirchhoff's rules. Express your answers using two significant figures separated by commas.

Explanation / Answer

Part A

R2 and R4 are in series: Req=R2+R4=6.3+11=17.3 ohm

Req is in parallel with R3 Req2=Req//R3=(17.3*6.1)/(17.3+6.1)=105.53/23.4=4.51 ohm

Req2 in series with R1 Req3=Req2+R1=13+4.51=17.51 ohm

the current in Req3 is I=18/17.51=1.03 A which is the same as in R1 so IR1=1.03 A

the voltage across R1 is VR1=1.03*13=13.39 V

so the voltage across Req2 is 18-13.39=4.61V

so the current in R3 IR3=4.63/6.1=0.76 A

and current in R2 and R4 is IR2=IR4=4.63/Req=4.63/17.3=0.26 A

Part B

KVL:

-18+ R3I3 +R1 I1=0 ==>-18+6.1I3+13I1=0

-R3I3+(R2+R4)I2=0==>-6.1I3+17.3I2=0 ==> I2=6.1/17.3 I3=0.35 I3

and KCL I1=I2+I3

-18+6.1I3+13I1=0

-18+6.1I3+13(I2+I3)=0

-18+6.1I3+13(0.35 I3+I3)=0

-18+6.1I3+17.55I3=0==> I3=18/(6.1+17.55)= 0.76A

I2=0.35*0.76= 0.26A

and I1=I2+I3=0.76+0.26=1.03A

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