Question

The current (I) in a wire varies directly as the voltage (v) and inversely as the resistance (r). If the current is 27.5 amps when the voltage is 110 volts and the resistance is 4 ohms, find the current when thevoltage is 180 volts and the resistance is 12 ohms. (Round your answer to two decimal places.)

Answer 1

From the information provided in the question, we have that the current (I) varies directly as the voltage (v). This is written mathematically to be:

$I\propto v$

It is also given that the current varies inversely as the resistance (r). This is written mathematically as:

$I\propto\frac{1}{r}$

Combining both relationships, we have that:

$I\propto\frac{v}{r}$

Applying a constant so that we can have an equation relating all 3 parameters, we have:

$I=\frac{kv}{r}$

If the current is 27.5 amps when the voltage is 110 volts and the resistance is 4 ohms, we have that:

$\begin{gathered} I=27.5 \\ v=110 \\ r=4 \end{gathered}$

Substituting these values into the equation to get the value of the constant, we have:

$\begin{gathered} 27.5=\frac{k\times110}{4} \\ k=\frac{27.5\times4}{110} \\ k=1 \end{gathered}$

Therefore, the equation becomes:

$I=\frac{v}{r}$

When the voltage is 180 volts and the resistance is 12 ohms, we can get the current by making the following substitution into the equation above and solving as follows:

$\begin{gathered} v=180 \\ r=12 \\ \therefore \\ I=\frac{180}{12} \\ I=15 \end{gathered}$

The current is 15.00 amps.