FIGURE EX32.24 shows voltage and current graphs for an inductor. What is the emf frequency f?

Verified step by step guidance

1. Step 1: Observe the graph provided. The voltage and current graphs are sinusoidal, indicating alternating current (AC). The frequency of the emf can be determined from the time period of the oscillations.
2. Step 2: Identify the time period of the voltage or current wave. From the graph, the voltage completes one full cycle between 0.00 s and 0.02 s. This means the time period T is 0.02 seconds.
3. Step 3: Recall the relationship between frequency and time period. The frequency f is the reciprocal of the time period T. The formula is: $f=\frac{1}{T}$
4. Step 4: Substitute the value of T into the formula. Since T = 0.02 s, the frequency f can be calculated using the formula above.
5. Step 5: Conclude that the frequency f is determined by the reciprocal of the time period, which is the number of cycles per second.

Key Concepts

Inductance

Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. The induced electromotive force (emf) in an inductor is proportional to the rate of change of current, which leads to a phase difference between voltage and current in AC circuits.

Phase Relationship

In AC circuits, the phase relationship between voltage and current is crucial for understanding how energy is transferred. For inductors, the voltage leads the current by 90 degrees, meaning that the peak voltage occurs a quarter cycle before the peak current. This phase difference affects the calculation of frequency and impedance in the circuit.

Frequency Calculation

Frequency is defined as the number of cycles of a periodic wave that occur in one second, measured in hertz (Hz). In the context of the provided graphs, the frequency can be determined by analyzing the time period of the voltage or current waveforms. The frequency is the reciprocal of the time period, allowing for the calculation of the emf frequency from the observed oscillations in the graphs.