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 time period of an alternating current is defined as:
- Where:
- T = time period (s)
- f = frequency (Hz)
- 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
Time period and peak current on a current-time 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.
Answer:
Step 1: Write down the period-frequency relation
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 is
T = 0.2 ms = 0.2 × 10-3 s
Step 3: Substitute into frequency equation
Examiner 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.