Final answer:
The amplitude of the current, I₀, represents the maximum or peak current in the expression I(t) = I₀ cos(ωt), where I(t) is the time-dependent current through an AC circuit.
Step-by-step explanation:
The amplitude of the current through the voltage source is given as I₀ in the expression I(t) = I₀ cos(ωt). This I₀ is the maximum or peak current that flows through the circuit and is a key parameter in describing oscillatory behaviors, such as those in AC circuits. In phasor notation, which is often used in AC circuit analysis, the current amplitude stands independent of time and represents the radius of the phasor's circular motion in a phasor diagram. The instantaneous current i(t) can also be represented as i(t) = I₀ sin (ωt - ϕ), where ω is the angular frequency and ϕ is the phase angle. Hence, the value of I₀ you are looking for is the coefficient in front of the sinusoidal function, and it represents the maximum value that the time-dependent current can achieve.
The amplitude of the current through the voltage source, given by the equation I(t) = I₀ cos(ωt), is equal to the coefficient of the cosine term, which is represented by I₀. This value represents the maximum current value or the peak current amplitude.