The potential difference applied across a given resistor is altered so

1.	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?
Answer» Heat generated H = I₂ Rt = \(\frac{V^2t}{R}\) Given, H = 9H \(\therefore \,\frac{V'^2}{t}=9\times\frac{V^2t}{R}\) \(\Rightarrow \) V² = 9 x V² \(\Rightarrow \) V' = \(\sqrt{9}\times V\) \(\therefore \,\,V=3V\) ∴ Potential difference increases by a factor of \(\sqrt{9}\) i.e., 3.

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?

Answer»

Heat generated H = I₂ Rt = \(\frac{V^2t}{R}\)

Given, H = 9H

\(\therefore \,\frac{V'^2}{t}=9\times\frac{V^2t}{R}\)

\(\Rightarrow \) V² = 9 x V² \(\Rightarrow \) V' = \(\sqrt{9}\times V\)

\(\therefore \,\,V=3V\)

∴ Potential difference increases by a factor of \(\sqrt{9}\) i.e., 3.