D2-SCT41: FOUR RESISTOR CIRCUITCURRENT In the circui shown, the sizes of the res

Question

D2-SCT41: FOUR RESISTOR CIRCUITCURRENT In the circui shown, the sizes of the resistors vary as R,>R,> R,>R. Four students discussing the currents in this circuit make the following statements: Ajay : "I think the current in R, will be the largest because all of the curreni from the battery goes through it." "Righi, and after R, the current splits into two parts at the junction. The current through R, R, and R, will all be the same because there are two branches in the circuit and each branch will get half of the current." "From Ohm's law, current is biggest where resistance is smallest. I think the current through R, will be largest because that branch has the lowest resistance in the circuit,'" "Also using Ohm's law, I think the current in R, will be the smallest because R, has the largest resistance. The current in R, will be largest, because that resistor has the smallest resistance." "The current in R, will be the same as the current in R, because they are in the same branch." Belen: Ciara Damaris Efren With which, if any, of these students do you agree? Ajay Explain your reasoning. Belen Damaris renNone of them Ciara

Explanation / Answer

Answer is Ajay and Efreen ,consider below example

Let us assume resistors according to R3>R1>R2>R4

R3 =400 ohms ,R1=300 ohms ,R2=200 ohms and R4 =100 ohms

and E=25 V

R3 and R4 are in series

R34 =400+100 =500 ohms

R34 and R2 are in parallel

1/R234 =1/500 +1/200

R234 =142.857 ohms

R1 and R234 are in series ,Therefore equivalent resistance

R=300+142.857 =442.857 ohms

Total current flowing in the circuit

I=E/R =25/442.857 =0.05645 A

Then current flowing through each resistor

I1=I=0.05645

Voltage across R1 is

V1=I1R1 =0.05645*300 =16.94 Volts

Voltage acorss R2,R3 and R4 is

V234=25-16.94 =8.06 V

I2=8.06/200 =0.04032 A

I3 = I4 =8.06/(400+100) =0.01613 A

Therefore I Agree with Ajay and Efren

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