How Does Power Dissipation in One Resistor Relate to Total Power from Batteries?

[Vibhor]

Homework Statement

Homework Equations

The Attempt at a Solution

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The first and foremost thing which I do not understand in this question is that there are many resistors present in the circuit , so how is it that we could relate power dissipated in one resistor to the power supplied by the batteries ??

But if I assume only one resistor , then I do get option a) .

Thanks

 

[cnh1995]

But if I assume only one resistor , then I do get option a) .

That's correct.

The first and foremost thing which I do not understand in this question is that there are many resistors present in the circuit , so how is it that we could relate power dissipated in one resistor to the power supplied by the batteries ??

When you make changes in the supply voltage, voltage across and current through each resistor in the network change proportionally. This is because resistors follow linear relation between V and I i.e. Ohm's law, irrespective of their configuration.