Question

In electronics, the formula V = IR is called Ohm's Law. It gives the relationship in a circuit between the voltage V (in volts), the current I (in amperes), and the resistance R (in ohms).Find R when I = 9 − 2i amperes and V = 38 + i volts.

Answer 1

V = IR is called Ohm's Law. It gives the relationship in a circuit between the voltage V (in volts), the current I (in amperes), and the resistance R (in ohms).

Step-by-step explanation:

Here we have a complex number operation. According to Ohm's law V=I*R, so:

`\begin{gathered} V=38+i \\ I=9-2i \end{gathered}`

`R=(V)/(I)=(38+i)/(9-2i)`

we need to remove the complex number on the denominator, so we have to multiply by its complement on both side

`\begin{gathered} (38+i)/(9-2i)*(9+2i)/(9+2i) \\ (342+76i+9i+2i^2)/(81+18i-18i-4i^2) \\ =(342+85i+2(-1))/(81-4(-1)) \end{gathered}`

where

`i^2=-1`
`\begin{gathered} (342+85i-2)/(81+4) \\ (340+85i)/(85) \\ (85(4+i))/(85) \\ 4+i \end{gathered}`

Therefore the answer is

`R=4+i`