Chapter 12.8, Problem 13P

a.

To determine

To calculate: The effect on the heat generated in the specific cases. The heat generated by a stove element varies jointly as the resistance and the square of the current.

The current is unchanged but the resistance is doubled.

Answer to Problem 13P

The statement is written as: “ $H=\left(2R\right)I^2$ ”doubled.

Explanation of Solution

Given information:

The effect on the heat generated in the specific cases. The heat generated by a stove element varies jointly as the resistance and the square of the current.

The current is unchanged but the resistance is doubled.

Formula used:

For the varies jointly:

  $H=KR{I}^2$

Calculation:

Consider the provided statement: The effect on the heat generated in the specific cases. The heat generated by a stove element varies jointly as the resistance and the square of the current.

Recall that, the current is unchanged but the resistance is doubled.

Then rewrite the statement as:

Current $I$ is unchanged but $R$ is doubled written as:

  $H=\left(2R\right)I^2$ .

Here the heat equals to the current is same but the resistance is doubled.

Thus, the statement is written as: “ $H=\left(2R\right)I^2$ ”doubled.

b.

To determine

To calculate: The resistance is unchanged but the current is doubled.

Answer to Problem 13P

The expression “ $4R{I}^2$ .” is quadrupled.

Explanation of Solution

Given information:

The effect on the heat generated in the specific cases. The heat generated by a stove element varies jointly as the resistance and the square of the current.

The resistance is unchanged but the current is doubled.

Formula used:

For the varies jointly:

  $H=KR{I}^2$

Calculation:

Consider the provided statement “The effect on the heat generated in the specific cases. The heat generated by a stove element varies jointly as the resistance and the square of the current.

Then rewrite the statement as:

The resistance is unchanged but the current is doubled.

Then rewrite the statement as:

Resistance $R$ is unchanged but current $I$ is doubled written as:

  $\begin{array}{c}H=R{\left(2I\right)}^2\\ H=R4I^2\\ H=4R{I}^2\end{array}$ .

Here the heat equals to the resistance is same but the current is doubled.

Thus, the statement is written as: “ $H=4R{I}^2$ ”quadrupled.

c.

To determine

To calculate: The current is tripled and the resistance is doubled.

Answer to Problem 13P

The statement is written as: “ $H=18R{I}^2$ ” $18$ times.

Explanation of Solution

Given information:

The effect on the heat generated in the specific cases. The heat generated by a stove element varies jointly as the resistance and the square of the current.

The current is tripled and the resistance is doubled.

Formula used:

For the varies jointly:

  $H=KR{I}^2$

Calculation:

Consider the provided statement The current is tripled and the resistance is doubled.

Then rewrite the statement as:

The current is tripled but the resistance is doubled.

Resistance $R$ is doubled but current $I$ is tripled then the equation is written as:

  $\begin{array}{c}H=2R\times {\left(3I\right)}^2\\ H=2R\times 9I^2\\ H=18R{I}^2\end{array}$ .

Here the heat equals to the resistance is doubled but the current is tripled so it is $18$ times.

Thus, the statement is written as: “ $H=18R{I}^2$ ” $18$ times.