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
- 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
Step 2:
Calculate the time period from the graph
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- The time period is the time taken for one complete cycle
- From the graph this is equation to 0.2 ms
- Therefore, the time period, T = 0.2 ms = 0.2 × 10-3 s
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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)
- Where:
- V = voltage (V)
- V0 = peak voltage (V)
- Recall the relation the equation for angular frequency ⍵:
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
Step 4: Substitute values into alternating current equation at time t
Using the time given in the question, t = 0.48 s
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