Question

electricity use the formula v = ci, where v is the voltage, c is the current, and i is the impedance. the current in a circuit is 2 + 4j amps, and the impedance is 3 - j ohms. what is the voltage?

Explanation:

Step1: Substitute values into formula

Given $C = 2 + 4j$ and $I=3 - j$, and $V = CI$, so $V=(2 + 4j)(3 - j)$.

Step2: Expand the product

Using FOIL method:
\[

$$\begin{align*} V&=(2\times3)+(2\times(-j))+(4j\times3)+(4j\times(-j))\\ &=6-2j + 12j-4j^{2} \end{align*}$$

\]

Step3: Simplify using $j^{2}=-1$

Since $j^{2}=-1$, we have $V = 6-2j + 12j-4\times(-1)$.
\[

$$\begin{align*} V&=6-2j + 12j + 4\\ &=(6 + 4)+(-2j+12j)\\ &=10 + 10j \end{align*}$$

\]

Answer:

$10 + 10j$ volts