Question

A resistor dissipates $2.0W$when the rms voltage of the emf is$10.0V$. At what $rms$voltage will the resistor dissipate $10.0W$$?$

Short answer

The $rms$voltage of the resistor at $P=10W$is =$10\sqrt{5}V$.

Step-by-step solution

Given information.

We have been given that,

$$\begin{gathered} P_1=2ohm \\ {P}_2=10ohm \\ {V}_{rm{s}_1}=10V \end{gathered}$$

We have to find$V_{rm{s}_2}$.

Simplify.

We use the formula ,

$P=\frac{({V_{rms})}^2}{R}$

We have to find$V_{rm{s}_2}$,

$\frac{P_1}{P_2}=\frac{{\left(V_{rm{s}_1}\right)}^2}{({V_{rm{s}_2})}^2}$

${\left(V_{rm{s}_2}\right)}^2=({V_{rm{s}_1})}^2\frac{P_2}{P_1}$

${\left(V_{rm{s}_2}\right)}^2={\left(10\right)}^2\frac{10}{2}$ $(Substitutingthevalues)$

${\left(V_{rm{s}_2}\right)}^2=100\times 5$

$\left(V_{rm{s}_2}\right)=10\sqrt{5}V$