Adding a resistor to a circuit does not always decrease the current in the circu

Question

Adding a resistor to a circuit does not always decrease the current in the circuit. Depending on how you add a resistor to a circuit, adding a resistor can increase the total current in the circuit, and/or increase the current in one part of the circuit. Consider the circuit shown below.

In order for the current through the 3.0 ? resistor to be maximized, you place an 11 ? resistor in parallel with the 4 ? resistor to create a new circuit. By how much does the current through the 3.0 ? resistor increase when you do this?

Explanation / Answer

in case 1

Reff = R1 +R2*R3(R2+R3)

Reff = 4 +3*6/9 = 6 ohm

i = V/Reff = 18/6 = 3 A

current through 3 ohm resistor be i1

voltage across 3 ohm resistor = 6V

i1 = 6/3 = 2A

when 11 ohm is connected parallel with 4 ohm resistor

Reff = R1*R4/(R1+R4) + R2*R3(R2+R3)

Reff = 2.9333 + 2 = 4.9333 ohm

i =V/Reff = 18/4.9333 = 3.64864 A

current through 3 ohm resistor be i2

voltage across 3 ohm resistor = 7.2973 V

i2 = 7.2973/3 =2.432432

increase in current is I = 2.432432 - 2 = 0.432432 A

I = 0.432432 A

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