Alternating Current & Voltage (AQA A Level Physics): Revision Note

Sinusoidal & Root-Mean-Square Current & Voltage

• 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 I_rms 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 V_rms 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

V_rms 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 = I_rms × V_rms

Applications of Alternating Current & Voltage

• 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