## Exploration 31.1: Amplitude, Frequency, and Phase Shift

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We characterize the voltage (or current) in AC circuits in terms of the amplitude, frequency (period), and phase. The sinusoidal voltage of this function generator is given by the equation

V (t) = V_{0} sin(ωt - φ) = V_{0} sin(2πƒt - φ),

where V_{0} is the amplitude, ƒ is the frequency (ω = 2πƒ is the angular frequency), and φ is the phase angle **(voltage is given in volts and time is given in seconds)**. Restart.

To begin with, keep the resistance of the variable resistor equal to zero. Pick values for the voltage amplitude (between 0 and 20 V), frequency (between 100 and 2000 Hz), and phase angle (between -2π and 2π).

- What does the amplitude on the graph correspond to?
- If you increase the amplitude, what do you expect to happen? Try it.
- Measure the time between two peaks (or valleys) on the graph. This is the period (T). What does 1/T equal?
- What do you need to change to increase the time between two peaks? Try it.
- Compare the plots when φ = 0 and when φ = 0.5*π. (You can right-click inside the plot to make a copy.)
- What happens when φ = π?
- Pick a value of φ other than 0. Measure the time, t (measured from t = 0), it takes for the graph to cross the horizontal axis with a positive slope (going up). φ should be equal to 2πƒt. So, the phase (or phase shift) tells you how much the graph is shifted from a straight sin2πƒt curve.
- Note that when φ = 0.5*π, the plot is a cosine curve. Why?

Now, change the variable resistor. The plot shows both the voltage across the 1000 Ω resistor **(blue)** and the voltage supply **(red)**. Kirchhoff's laws hold for any instant of time in an AC circuit.

- Use the techniques you learned for DC circuits to calculate the current in the circuit at several different points.
- Verify that this circuit is simply a voltage divider.
- What value does the variable resistor need to have for the maximum voltage across the 1000-Ω resistor to be 1/3 of the value of the source?

Exploration authored by Anne J. Cox.

Script authored by Wolfgang Christian.