PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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The Potential Difference Applied Across a Given Resistor is Altered So that the Heat Produced per Second Increases by a Factor of 9. by What Factor Does the Applied Potential Difference Change? - PUC Karnataka Science Class 12 - Physics

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Question

The potential difference applied across a given resistor is altered so that the heat produced per second increases by a factor of 9. By what factor does the applied potential difference change?

Solution

We know, the heat (H) produced across a resistor in time t due to flow of current (I) through it is

`H =V^2/Rt`

where, V is the potential difference applied across resistor R which gives current I.

Therefore, heat produced per second is

`H/t =V^2/R`

`⇒V^2 prop H or V prop sqrtH `    ...(i)

Now when the potential difference is altered from V to say V', then the heat produced per second increases by factor of 9

`⇒V' prop sqrt(9H)`

`or V' prop 3sqrtH`     ...(ii)

Dividing (i) by (ii), we get

`(V')/V = (3sqrtH)/sqrtH`

`⇒V' = 3 V`

Hence, the potential difference changes by a factor of 3.

  Is there an error in this question or solution?
Solution The Potential Difference Applied Across a Given Resistor is Altered So that the Heat Produced per Second Increases by a Factor of 9. by What Factor Does the Applied Potential Difference Change? Concept: Electric Potential Difference.
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