# 26.1.1 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: • 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 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. Use the graph to calculate the frequency of the supply.

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 #### 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 = V0 sin(⍵t)

#### Worked Example

An alternating current I varies with time t as shown in the graph below. 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 = I0 sin(⍵t)

Step 2:            Write out the equation for angular frequency 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

#### 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 ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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