PLEASE ANSWER PART A AND B AND SHOW WORK I WILL REPORT YOU IF YOU WRITE NONSENSE

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PLEASE ANSWER PART A AND B AND SHOW WORK I WILL REPORT YOU IF YOU WRITE NONSENSE OR DO NOT ANSWER THE QUESTION: if the answer is wrong because you wrote nonsense you will be reported.

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.

(a) How would you add a resistor with a resistance of 9.00 to the circuit so that the current through the 3.0 resistor is maximized?

A.)Put the new resistor in series with the 4 resistor.

B.)Put the new resistor in parallel with the battery.    

C.)Put the new resistor in parallel with the 4 resistor.

D.) Put the new resistor in series with the 3 resistor.

E.)Put the new resistor in series with the 6 resistor.

F.) Put the new resistor in parallel with the 3 and 6 resistors.

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

The current increases by _____ A

Explanation / Answer

remember these about Combination of Resistors

if R1 and R2 are the resistances connected in series then effective resiatcne Rnet = R1+R2

if R1 and R2 are connected in parallel, then 1/Rnet =1/R1 +1/R2 or Rnet = R1R2/(R1+R2)

same current passes through each of the ressitor in series combination and

same votage passes through eacf of the resistor in parallel combination

apply ohms law V = iR

where V = volatge and i = current

so pART A:

to maximise the current, Resistance in the ckt has to be minimised

this is acheived by connecting 9 ohms resisotr must be connected in parallel

correct option is F.) Put the new resistor in parallel with the 3 and 6 resistors.
----------------------------------

intially Rnet = 3 // 6 + 4

Rnet = 3*6/9 + 4 = 6 ohms

current i = V/R = 18/6 = 3 ohms

after 9ohms is added ,

Rnet = 4 + (3 // 6 // 9)

Rnet = 5.64 ohms

so

Imax = V/R = 18/5.64 = 3.2 Amps

so current increases by 0.2 Amps

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