Chapter 7.4, Problem 62PPS

a.

To determine

To simplify the given formula

Answer to Problem 62PPS

  $P=I^{2}R$

Explanation of Solution

Given:

  $I=\sqrt{\frac{P}{R}}$

P is the power in Watts.

R is the mass of the ball resistance in Ohms.

I is the current in amperes.

Calculation:

Now, $I=\sqrt{\frac{P}{R}}$

  $\Rightarrow I^2={\left(\sqrt{\frac{P}{R}}\right)}^2[\because \text{Squaring on both sides}]$

  $\begin{array}{l}\Rightarrow I^2=\frac{P}{R}\\ \Rightarrow P=I^{2}R\end{array}$

Conclusion:

Hence, the simplified form according to the given situation will be: $P=I^{2}R$

b.

To determine

To identify the current that appliance uses.

Answer to Problem 62PPS

  $\sqrt{15}$ Amperes

Explanation of Solution

Given:

  $P=I^{2}R$

P is the power in Watts.

R is the mass of the ball resistance in Ohms.

I is the current in amperes.

Calculation:

Let,

  $P=I^{2}R\mathrm{...................}(i)$

Given that,power consumed by appliance is 75 Watts and Resistance is 5 Ohms, which means,

  $P=75$ and $R=5$

Now, substituting the value of P and R in equation ( i ),

  $\begin{array}{l}\Rightarrow 75=I^2\times 5\\ \Rightarrow I^2=\frac{75}{5}\\ \Rightarrow I=\sqrt{15}\end{array}$

Conclusion:

Hence, the required current is $\sqrt{15}$ Amperes.