Question

The voltage V (in volts) across any element in an AC circuit is calculated as a product of the current I and the impedance Z (in ohms) = V=IZ.

a) Find the voltage in a circuit with a current I=3-2i amperes and an impedance of Z = 5 + 5i ohms.

Answer 1

The voltage in an AC circuit with a current of 3 - 2i amperes and an impedance of 5 + 5i ohms is calculated using the formula V=IZ, yielding a voltage of 25 + 5i volts.

Step-by-step explanation:

To find the voltage in an AC circuit with a given current and impedance, we can use the formula V = IZ. The current (I) is given as 3 - 2i amperes and the impedance (Z) is 5 + 5i ohms. To calculate the voltage (V), we perform the multiplication of the complex numbers.

V = (3 - 2i) × (5 + 5i)

First, multiply the real parts:

3 × 5 = 15

Now, multiply the imaginary parts and the result by i² (remembering that i² = -1):

(-2i) × (5i) = -10i² = 10

Multiply the cross terms:

3 × 5i + (-2i) × 5 = 15i - 10i = 5i

Now, combine the real parts and the imaginary parts:

V = 15 + 10 + 5i

V = 25 + 5i volts

So the voltage across the element in the AC circuit is 25 + 5i volts.