91Ó°ÊÓ

Alternating Current, often abbreviated as AC, is a type of electrical current where the flow of electric charge periodically reverses direction. This is different from Direct Current (DC), where the flow of electric charge is only in one direction. The advantage of AC is that it is easier to transform into different voltages, making it very suitable for power supply over long distances.
In terms of the mathematical expression, as seen in the exercise, AC is typically described using sine or cosine waves. The current given in the problem, for instance, uses a sine wave: \[I(t) = (0.707 ext{A}) \sin[(314 ext{Hz}) t]\]This signifies that as time changes, so does the direction and magnitude of current flow. AC is widely used in household electrical systems, mostly because of its efficient transmission qualities.

Ohm's Law is a fundamental principle in circuit analysis. It relates the voltage (\(V\)), current (\(I\)), and resistance (\(R\)) in a linear electric circuit. The law is succinctly expressed with the equation:\[V = IR\]This equation tells us that the voltage across a conductor is proportional to the current flowing through it, which in turn is directly proportional to the resistance. In the context of the exercise, we utilized Ohm’s Law to find the resistance of the bulb's filament.
Since the problem provides RMS values for the current and voltage, we rewrite the equation as:\[R = \frac{V}{I_{\text{rms}}}\]Knowing the RMS current is approximately \(0.5 \, ext{A}\) and the voltage is \(120 \, ext{V}\), we determine the resistance to be \(240 \, \Omega\).

Power calculation is a process used to determine the amount of electrical power needed or consumed by a device. It's an important concept as it tells us how much energy a device uses over time. The basic formula for calculating electrical power in an AC circuit is:\[P = V_{\text{rms}} I_{\text{rms}}\]In the exercise, we need to calculate the average power delivered to a light bulb. We know from the previous steps:

• RMS Voltage (\(V_{\text{rms}}\)): 120 V
• RMS Current (\(I_{\text{rms}}\)): 0.5 A

Plugging these values into the power formula gives:\[P = 120 \, \text{V} \times 0.5 \, \text{A} = 60 \, \text{W}\]This tells us the average power used by the bulb is 60 watts, indicating how much the electrical energy it transforms into light and heat every second.

Frequency is a measure of how many cycles of an AC signal occur per second. It is measured in hertz (Hz), where one hertz equals one cycle per second. Frequency is a critical concept in AC circuits as it determines the behavior of the circuit and the types of appliances that can be used.
In the exercise, we calculated the frequency using the relationship between angular frequency \(\omega\) and standard frequency \(f\). The angular frequency \(\omega\) is given as 314 Hz. Frequency is calculated as:\[\omega = 2\pi f \f = \frac{\omega}{2\pi} = \frac{314}{2\pi} \approx 50 \, \text{Hz}\]A frequency of 50 Hz is typical for AC power systems in many parts of the world, indicating 50 cycles per second.