A full set of ten original structured questions in the style of Paper 4, covering the whole of Alternating currents: peak and r.m.s. values, mean power, and half-wave, full-wave and smoothed rectification. Several questions carry the characteristics of a.c. into the rectifier that follows. Each is linked to its lessons; attempt them all, then reveal the worked solutions.
A sinusoidal current is described by i = I₀ sinωt, with a peak value of 8.0 A and a frequency of 50 Hz.
(a) State what is meant by the peak value. [1]
(b) Calculate the r.m.s. value of the current. [2]
(c) Calculate the period of the current. [1]
(d) Calculate the angular frequency ω. [2]
(e) Write the equation for the current with these numerical values. [1]
(f) Calculate the current at t = 5.0 ms. [2]
(g) State the time at which the current first returns to zero after t = 0. [1]
A heating element of resistance 46 Ω is connected to the 230 V (r.m.s.), 50 Hz mains supply.
(a) Calculate the peak voltage of the supply. [2]
(b) Calculate the r.m.s. current in the element. [2]
(c) Calculate the mean power dissipated. [2]
(d) Calculate the peak power dissipated. [2]
(e) State the ratio of mean power to peak power. [1]
(f) State why r.m.s. values, rather than the simple average, are quoted for a.c. [1]
A resistor of resistance 12 Ω carries a sinusoidal current of peak value 3.0 A.
(a) Calculate the r.m.s. current. [2]
(b) Calculate the mean power dissipated in the resistor. [2]
(c) Calculate the peak (maximum instantaneous) power. [2]
(d) State the relationship between the mean power and the peak power. [1]
(e) State the value of the steady direct current that would dissipate the same mean power. [2]
Fig. 4.1 shows how an alternating current varies with time.
(a) State the peak value of the current. [1]
(b) Read the period from the graph and hence calculate the frequency. [2]
(c) Calculate the angular frequency ω. [2]
(d) Write the equation of the current in the form i = I₀ sinωt. [1]
(e) Calculate the r.m.s. value of the current. [2]
(f) State the time at which the current first reaches its peak. [1]
A single diode is connected in series with a resistor and a sinusoidal a.c. supply.
(a) Explain how the diode produces half-wave rectification. [2]
(b) Describe the output voltage across the resistor over one cycle. [2]
(c) State the fraction of each cycle during which current flows in the resistor. [1]
(d) Explain why the mean power delivered is less than for full-wave rectification of the same supply. [2]
(e) State one disadvantage of half-wave rectification. [1]
Fig. 6.1 shows the output of a full-wave rectifier (no smoothing) supplied from 50 Hz a.c.
(a) State the number of diodes in a bridge rectifier. [1]
(b) Explain how the bridge produces full-wave rectification. [3]
(c) State the frequency of the output shown in Fig. 6.1, and explain your answer. [2]
(d) State one advantage of full-wave over half-wave rectification. [2]
A capacitor is added to the output of a rectifier to smooth it.
(a) State how the smoothing capacitor is connected relative to the load. [1]
(b) Explain how the capacitor smooths the output. [3]
(c) State and explain the effect on the ripple of using a larger capacitance. [2]
(d) State the effect on the ripple of increasing the load resistance. [1]
(e) State what the output would be if the load were disconnected entirely. [1]
An a.c. supply of r.m.s. value 12 V and frequency 50 Hz is connected to a single-diode (half-wave) rectifier and a load. Parts (a) and (b) use the a.c. characteristics; the rest use rectification.
(a) Calculate the peak voltage of the supply. [2]
(b) Stating any assumption, give the peak output voltage across the load. [1]
(c) For how long in each cycle does the diode conduct? [2]
(d) A smoothing capacitor is now connected across the load. Describe the output. [2]
(e) State the ripple frequency of this smoothed half-wave output. [1]
A full-wave rectifier supplied from 50 Hz a.c. feeds a load of resistance 2.2 kΩ with a smoothing capacitor of 100 μF in parallel.
(a) Calculate the time constant of the load and capacitor. [2]
(b) State the frequency and period of the ripple before smoothing. [2]
(c) By comparing the time constant with the ripple period, explain whether the smoothing is effective. [2]
(d) State and explain the effect of replacing the capacitor with a 470 μF one. [2]
This question follows a power supply from end to end. A transformer secondary provides 9.0 V (r.m.s.) at 50 Hz to a bridge rectifier, whose output is smoothed and connected to a load.
(a) Calculate the peak voltage at the secondary. [2]
(b) State the type of rectification and the number of diodes used. [2]
(c) State the ripple frequency of the rectified output. [2]
(d) A smoothing capacitor is added across the load. Describe the output voltage. [2]
(e) The load is changed to draw a larger current (a smaller resistance). State and explain the effect on the ripple. [3]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.