Question

The voltage across 10-ohm resistor is 25 sin (377 t+60°) V. Find the current i(t) through the resistor, then express it in a phasor form

iᵣ(t) =

Answer 1

The current i(t) through the 10-ohm resistor is given by 2.5 sin(377t + 60°) A, and its phasor form is 2.5∠60° A

Step-by-step explanation:

The voltage across a 10-ohm resistor is given by 25 sin(377t + 60°) V. To find the current i(t) through the resistor, we can apply Ohm's law, which states that voltage (V) equals current (I) multiplied by resistance (R), V = IR. Therefore:

i(t) = V(t) / R

By substituting the given values:

i(t) = (25 sin(377t + 60°) V) / (10 Ω)

i(t) = 2.5 sin(377t + 60°) A

To express the current in phasor form, we simply take the amplitude and the phase angle:

iᵢ(t) = 2.5∠60° A