#### 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.