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I have the question "Two resistors of resistance, 3 ohms and 6 ohms, are connected in parallel across a battery having a voltage of 12V."

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I am asked to determine the total circuit resistance. Here is my attempt is this correct ?

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It then asks me to find the current flowing in the 3 ohm resistor using the answer above. For which I got:

V = IR

Therefore , I = V/R

Therefore,

I = 12/2 = 6A

Is this correct also ?

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Yes, your answers are 100% correct.

If you want to do a bit of a cross check, calculate the current through each resistor individually and add them.

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Yes, both answers are correct.

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