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.

If you add a resistor with a resistance of 9.00 to the circuit then we put the new resistor in parallel with the 4 resistor.

GIVEN THIS INFORMATION:

By how much does the current through the 3.0 resistor increase when you do that?

The current increases by _____ A

Explanation / Answer

Initially

Req = R1 + (R2*R3/(R2+R3))

Req = 4 + 6*3/(6+3) = 4 + 2

Req = 6 ohm

V = 18 V

I = V/R = 18/6 = 3 amp

In series circuit current is same and in parallel circuit voltage is same.

So Voltage through 3 ohm circuit is V = I*Req = 3*Req = 3*2 = 6V

current through 3 ohm is

I = 6/3 = 2 amp

In second Condition.

Req = 9*4/(9+4) + 6*3/(6+3) = 4.76 ohm

Current through circuit is I = 18/4.76 = 3.78 amp

So Voltage through 3 ohm circuit is V = I*Req = 3.78*Req = 3*2 = 7.56 V

current through 3 ohm is

I = 7.56/3 = 2.52 amp

So current incrases by 2.52 - 2 = 0.52 amp.

I understand that you added 9 ohm in parrallel to 4 ohm. assuming that i solved this question.

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