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. How would you add a resistor with a resistance of 10.0 ohm to the circuit so that the current through the 3.0 ohm resistor is maximized? By how much does the current through the 3.0 ohm resistor increase when you do that?

Explanation / Answer

if we put the new resistor in series with the 6 ohm resistor then we will get maximum current through 3 ohm.

now equivalent resistance = 4 + 3*(6+10)/(3+6+10) = 6.52 ohm

current through battery = 18/6.52 = 2.76 amp

now current through 3 ohm = 2.76*(6+10)/(3+6+10) = 2.32 amp

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