Final answer:
To find the sinusoidal expression for the current through a 1.8H coil with a voltage of 8sin(50t+65°), we calculate the inductive reactance and use Ohm's law for AC circuits.
Step-by-step explanation:
To solve the schoolwork question about the sinusoidal expression for the current in a circuit with an AC voltage source and an inductor, we must apply the concept of inductive reactance. The voltage across an inductor can be described as V = L di/dt, where L is the inductance and di/dt is the rate of change of current. The inductive reactance X₀L is ωL where ω is the angular frequency of the AC source. For the given voltage V(t) = 8sin(50t+65°), we can identify ω as 50 rad/s. Given L is 1.8 H, we can find the inductive reactance and use Ohm's law for AC circuits to find the current I(t). The inductive reactance X₀L will be ωL = 50 × 1.8 = 90 Ω. Ohm's law for AC circuits relates the voltage and the current by V(t) = I(t) × X₀L. Solving for I(t) gives us I(t) = V(t) / X₀L = 8sin(50t+65°) / 90 Ω. Simplifying gives us the sinusoidal expression for the current I(t) = (8/90)sin(50t+65°) A.