Alternating Current & Voltage (Cambridge (CIE) A Level Physics)

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

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.

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.

Answer:

Step 1: Write out the equation for alternating current

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

These equations are written as  , the x is replaced with I or V, depending on the question.

Remember to check that your calculator is in radians mode when using any of these equations. This is because the angular frequency ⍵ is measured in rad s^-1.

Current can also be positive or negative, depending on its direction. This is why the answer in the worked example is negative. At t = 0.48 s the current will be in the negative direction. The mark schemes in the exams are normally not too picky about this, but the size of the current (16 A in the worked example) is what will get the mark.