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

A current which periodically varies between a positive to a negative value 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?for a.c is:

• 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 a current-time or voltage-time graph
• The?peak-to-peak?current or voltage is the distance between a positive and consecutive negative peak. This means:

peak voltage V0?= peak-to-peak voltage ÷ 2

Graph of alternating current against time showing the time period, peak current and peak-to-peak current

Root-Mean-Square Current & Voltage

• Root-mean-square (rms) values of current, or voltage, are a useful way of?comparing?a.c current, or voltage, to its equivalent direct current (d.c), or voltage
• The rms values represent the direct current, or voltage, values that will produce the same?heating effect, or power dissipation, as the alternating current, or voltage
• The rms value of an alternating current is defined as:

The square root of the mean of the squares of all the values of the current in one cycle

• Or:

The equivalent direct current that produces the same power

• The rms current?Irms?is defined by the equation:

• Where:
  • I0?=?peak current?(A)

   

• The rms value of an alternating voltage is defined as:

The square root of the mean of the squares of all the values of the voltage in one cycle

• Or:

The equivalent dc voltage that produces the same power

• The rms voltage?Vrms?is defined by the equation:

• Where:
  • V0?=?peak voltage?(V)

   

• Rms current is equal to 0.707 ×?I0, which is about 70% of the peak current I0
  • This is also the case for rms voltage

   

• The rms value is therefore defined as:

The steady direct current, or voltage, that delivers the same average power in a resistor as the alternating current, or voltage

• A resistive load is any electrical component with resistance eg. a lamp

Vrms?and peak voltage. The rms voltage is about 70% of the peak voltage

• The average?power?of a supply is the product of the rms current and voltage:

Average power = Irms?× Vrms

Step 1: Write down the Vrms?equation

Step 2: Rearrange for the peak voltage,?V0

V0?= √2 × Vrms

Step 3: Substitute in the values

V0?= √2 × 230

Step 4: Calculate the peak-to-peak voltage

• • The peak-to-peak voltage is the peak voltage (V0) × 2

   

Peak-to-peak voltage = (√2 × 230) × 2 = 650.538 =?651 V (3 s.f)

• Mains electricity is supplied as alternating current by the National Grid
• This means that power stations produce alternating current
  • This is the type of current supplied when devices are plugged into sockets

   

• In the UK, the mains electricity supplied to households is 230 V at 50 Hz. This is its rms value
  • However, this varies depending on the customer (larger buildings and factories will require more)

   

• The mains voltage varies throughout the day depending on the demand and supply of electricity
• It is only lamps, heaters, cookers and devices with large electric motors (such as vacuum cleaners) that use a.c from the mains
• Most other devices such as televisions, computers and games consoles work with d.c
  • This means they are built with a step-down transformer that converts the 230 V a.c into (for example) 12 V d.c

   

• The peak and peak-to-peak values for the current and voltage for mains electricity are used to calculate the rms value and vice versa