CIE A Level Physics复习笔记21.1.1 Alternating Current & Voltage

Properties of Alternating Current & Voltage

  • An alternating current (a.c) is defined as:

A current which periodically varies from positive to negative and changes its magnitude continuously with time

  • This means the direction of an alternating current varies every half cycle
  • The variation of current, or p.d., with time can be described as a sine curve ie. sinusoidal
    • Therefore, the electrons in a wire carrying a.c. move back and forth with simple harmonic motion
  • As with SHM, the relationship between time period T and frequency  f of an alternating current is given by:

Properties of Alternating Current & Voltage equation 1

  • Peak current (I0), or peak voltage (V0), is defined as:

The maximum value of the alternating current or voltage

  • Peak current, or voltage, can be determined from the amplitude of the graph

Alternating current graph, downloadable AS & A Level Physics revision notes

Graph of alternating current against time with a time period of 20 ms and peak current of 2 A

  • Mains electricity is supplied as alternating current
    • Power stations produce alternating current
    • This is the type of current supplied when devices are plugged into sockets

Worked Example

The variation with time t of the output voltage V of an alternating voltage supply is shown in the graph below.Worked example voltage graph, downloadable AS & A Level Physics revision notes

Use the graph to calculate the frequency of the supply.

Step 1:           

Write down the period-frequency relation

Properties of Alternating Current & Voltage Worked Example equation 1

Step 2:           

Calculate the time period from the graph

      • The time period is the time taken for one complete cycle
      • From the graph, this is equal to 0.2 ms
      • Therefore, the time period, T = 0.2 ms = 0.2 × 10-3 s

Step 3:           

Substitute into frequency equation

Properties of Alternating Current & Voltage Worked Example equation 2

Exam Tip

Remember to double check the units on the alternating current and voltage graphs. These are often shown in the range of milli-seconds (ms) instead of seconds (s) on the x axis.

Using Sinusoidal Representations

  • The equation representing alternating current which gives the value of the current I at any time t is:

I = I0 sin(⍵t)

  • Where:
    • I = current (A)
    • I0 = peak current (A)
    • ⍵ = angular frequency of the supply (rad s-1)
    • t = time (s)
  • Note: this a sine function since the alternative current graph is sinusoidal
  • A similar equation can be used for representing alternating voltage:

V = Vsin(⍵t)

  • Where:
    • V = voltage (V)
    • V0 = peak voltage (V)
  • Recall the relation the equation for angular frequency ⍵:

Using Sinusoidal Representations equation 1

Worked Example

An alternating current I varies with time t as shown in the graph below.Worked example alternating current graph, downloadable AS & A Level Physics revision notes

Using the graph and the equation for alternating current, calculate the value of the current at a time 0.48 s.

Step 1:            Write out the equation for alternating current

I = Isin(⍵t)

Step 2:            Write out the equation for angular frequency

Using Sinusoidal Representations Worked Example equation 1

Step 3:            Measure the time period T and peak current I0 from the graph

The time period is the time taken for one full cycle, T = 0.10 s

Peak current (amplitude), I0 = 17 A

Step 4:            Substitute values into alternating current equation at time t

Using the time given in the question, t = 0.48 s

Using Sinusoidal Representations Worked Example equation 2

Using Sinusoidal Representations Worked Example equation 3

Exam Tip

Remember to check that your calculator is in radians mode when using any of these equations. This is because angular frequency ⍵ is measured in rad s-1

 

 

 

 

 

 

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