Paper 4 Alternating Current Answers

Q1 Oscilloscope Measurement

1. The amplitude is $2.8$ divisions, so $V_0=(2.8)(1.5)=4.2\mathrm{V}$. [2]

2. One cycle spans $4.0$ divisions:

   $$T=(4.0)(0.50\mathrm{ms})=2.0\mathrm{ms},f=\frac{1}{T}=5.0\times 10^2\mathrm{Hz}.$$

   [3]

3. $V_{\mathrm{rms}}=V_0/\sqrt{2}=4.2/\sqrt{2}=3.0\mathrm{V}$ (2 s.f.). [2]

4. The absolute uncertainty in locating the two end points is similar, but the measured interval is larger; dividing by the number of cycles therefore gives a smaller fractional uncertainty in one period. [2]

5. Increase vertical sensitivity and/or reduce the time-base setting so the trace occupies more of the screen while remaining fully visible. [1]

Q2 Rectifier Output Investigation

1. Display input and output traces or compare separate traces; half-wave has gaps for one half-cycle, full-wave has both half-cycles folded to one polarity. [2]
2. The capacitor reduces ripple: peaks are less separated by deep falls, giving a smoother p.d. [2]
3. Use an isolation transformer/low-voltage signal generator and avoid touching live circuits. [1]