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.
