7.5.5 Alternating currents

Alternating Current (AC) and Electromagnetic Induction

• When a coil rotates in a magnetic field, an electromotive force (emf) is induced due to the interaction between the magnetic field and the rotating coil.

• This induced emf can be calculated using:

$$\varepsilon = BAN\omega \sin(\omega t)$$

Where:

• $B$ is the magnetic flux density,
• $A$ is the area of the coil,
• $N$ is the number of turns in the coil,
• $\omega$ is the angular speed of the coil, and
• $t$ is time.
• The sine function indicates that the emf is alternating, meaning its direction changes over time as the coil rotates.

Understanding Oscilloscope Displays for AC and DC Currents

• An oscilloscope can display variations in voltage over time, useful for analysing both alternating and direct currents.
• The time-base setting controls the horizontal axis, showing how voltage changes over time:
  • With time-base on: All voltage variations are visible, displaying an AC waveform as a sinusoidal wave and DC as a straight line.
  • With time-base off: All voltages are displayed at once, showing AC as a vertical line and DC as a dot on the screen.
• Adjusting the Y-gain (for voltage) and time-base (for time intervals) makes measurements easier.

AC Waveforms and Measurements

1. Peak Voltage $(V_0)$: The highest point of the waveform from the zero or equilibrium position.
2. Peak-to-Peak Voltage: The voltage difference from the highest to the lowest point of the waveform.
3. Root Mean Square (RMS) Voltage: The effective voltage value of an AC supply. For a sinusoidal wave:

$$V_{\text{rms}} = \frac{V_0}{\sqrt{2}}$$

Similarly, the RMS current:

$$I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$$

4. Time Period (T): The time taken for one complete oscillation or cycle of the wave. The frequency ($f$) is the reciprocal of the time period:

$$f = \frac{1}{T}$$