Respuesta :
Answer:
41.99 or 42.0 volts.
Step-by-step explanation:
We have been given the impedance (Z) of the circuit which is:
[tex]Z=3.342+4.176i[/tex]
and the current through the circuit is:
[tex](5.772-5.323i)[/tex]
The voltage across the circuit is given by:
[tex]V= I\times Z=IZ[/tex], where 'V' is the voltage, 'I' is the current, and 'Z' is the impedance.
Plugging the values of 'I' and 'Z' we get:
[tex]V=(5.772-5.323i)\times 10^{-3}\times (3.342+4.176i)\times 10^3[/tex]
[tex]V=(5.772-5.323i)\times(3.342+4.176i)[/tex]
[tex]V= (41.51+6.31i)[/tex]
Now that we have the voltage, we can find the magnitude of the voltage as follows:
[tex]V= \sqrt{(41.51)^2+(6.31)^2}=\sqrt{1723.08+39.81}=\sqrt{1762.89}=41.98 \approx 42.0[/tex]
So the magnitude of the voltage across the circuit is 42.0 Volts.
