CAIE A-Level Physics A2 21 Alternating Currents Questions

Practise analysing sinusoidal a.c. values and power, rectification paths and smoothing behaviour in a practical rectified supply.

Exam points

calculate and interpret sinusoidal current and voltage parameters, rms values and power
analyse half-wave/full-wave rectification and diode conduction paths
explain and calculate smoothing behaviour in rectified supplies

Covered syllabus points

21.1 Characteristics of alternating currents 21.2 Rectification and smoothing

[Maximum number: 4]

(a)

The output of a power supply is represented by:

V=9.0 \sin 20 t

where V is the potential difference in volts and t is the time in seconds.
Determine, for the output of the supply:

[ 3 ]

(i)

the root-mean-square (r.m.s.) voltage, $V_{\text {r.m.s }}$ .

V_{\text {r.m.s }}=

[ 1 ]

$9.0 / \sqrt{ } 2=$
6.4 V

(ii)

the period T.

[ 2 ]

$\begin{aligned} \omega=20 \omega=2 \pi / T T=2 \pi / 20 \end{aligned}$ $T=0.31 \mathrm{~s}$

(b)

The variations with time t of the output potential difference V from two different power supplies are shown in Fig. 9.1 and Fig. 9.2.

Fig. 9.1

Fig. 9.2

The graphs are drawn to the same scale.
State and explain whether the same power would be dissipated in a $1.0 \Omega$ resistor connected to each power supply.

[ 1 ]

[Maximum number: 10]

Four diodes are used in a bridge rectifier circuit to produce rectification of a sinusoidal a.c. input voltage $V_{\text {IN }}$ .
Fig. 7.1 shows part of the circuit, but three of the diodes are missing.

Fig. 7.1

The p.d. across the load resistor R is the output p.d. $V_{\text {OUT }}$ of the bridge rectifier.

(a)

State the name of the type of rectification produced by a bridge rectifier.

[ 1 ]

(b)

Complete Fig. 7.1 by drawing the three missing diodes, correctly connected.

[ 2 ]

(c)

On Fig. 7.1, draw an arrow to indicate the direction of the current in resistor R .

[ 1 ]

(d)

$V_{\text {IN }}$ has amplitude $V_{0}$ and period T. Fig. 7.2 shows the variation with time t of $V_{\text {IN }}$ .

Fig. 7.2

[ 6 ]

(i)

On Fig. 7.3, sketch the variation of $V_{\text {OUT }}$ with t between t=0 and t=2.0 T.

Fig. 7.3

[ 3 ]

sketch: periodic line showing minimum $V_{\text {OUT }}=0$ and maximum $V_{\text {OUT }}=+V_{0}$
line showing peak $V_{\text {OUT }}$ at t=0,0.5 T, 1.0 T, 1.5 T and 2.0 T, with $V_{\text {OUT }}$ going to zero half-way in between each peak
line showing correct modulated sine shape

(ii)

The power dissipated in the resistor is P.

On Fig. 7.4, sketch the variation of P with t between t=0 and t=2.0 T.

Fig. 7.4

[ 2 ]

(iii)

Suggest, with a reason, how the root-mean-square (r.m.s.) value of $V_{\text {OUT }}$ compares with the r.m.s. value of $V_{\text {IN }}$ .

[ 1 ]

same power-time graph with or without rectification, so same $V_{\text {rms }}$

or

$V^{2}$ -time graph is same for both $V_{\text {OUT }}$ and $V_{\text {IN }}$ , so same $V_{\text {rms }}$

or

power does not depend on sign of V, so same $V_{\text {rms }}$

[Maximum number: 6]

(a)

Two coils of insulated wire are wound on an iron bar, as shown in Fig. 8.1.

Fig. 8.1

There is a current $I_{1}$ in coil 1 that varies with time t as shown in Fig. 8.2.

Fig. 8.2

[ 6 ]

(i)

The variation with t of $I_{1}$ can be represented by the equation

I_{1}=X \sin Y t

where X and Y are constants.

Use Fig. 8.2 to determine the values of X and Y. Give units with your answers.

\begin{aligned} & X=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . . . u n i t \\ & Y=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . u n i t \end{aligned}

[ 3 ]

$X=0.85 \mathrm{~A}$ $Y=2 \pi / 0.040$ $=160 \mathrm{rad} \mathrm{s}^{-1}$

(ii)

The current in coil 1 gives rise to a magnetic field in the iron bar.

Assume that the flux density of this magnetic field is proportional to $I_{1}$ .
An alternating electromotive force (e.m.f.) is induced across coil 2. The p.d. across coil 2 is measured using the voltmeter and has a root-mean-square (r.m.s.) value of 4.6 V .

On Fig. 8.3, sketch a line to show the variation with t of $V_{2}$ between t=0 and $t=0.08 \mathrm{~s}$ .

Fig. 8.3

[ 3 ]

two cycles of a sinusoidal curve with a period of 0.040 s
correct phase (i.e. $V_{2} \max / \min$ at t=0,0.02,0.04,0.06 and 0.08 s , and $V_{2}$ zero at $t=0.01,0.03,0.05,0.07 \mathrm{~s}$ )
maximum / minimum $V_{2}$ shown (consistently) at $\pm 6.5 \mathrm{~V}$

[Maximum number: 5]

Part of an electric circuit is shown in Fig. 5.1.

Fig. 5.1

The circuit is used to produce half-wave rectification of an alternating voltage of potential difference (p.d.) $V_{\text {IN }}$ .

The output p.d. across the $14 \mathrm{k} \Omega$ resistor is $V_{\text {OUT }}$ .

(a)

A component is missing from the circuit of Fig. 5.1.

Complete the circuit diagram in Fig. 5.1 by adding the circuit symbol for the missing component, correctly connected.

[ 1 ]

(b)

A capacitor C is shown in the circuit of Fig. 5.1.

State the effect on $V_{\text {OUT }}$ of including the capacitor in the circuit.

[ 1 ]

smoothing / $V_{\text {out }}$ is smoothed

(c)

Fig. 5.2 shows the variation with time t of $V_{\text {IN }}$ .

Fig. 5.2

Fig. 5.3 shows the variation with t of $V_{\text {OUT }}$ .

Fig. 5.3

[ 1 ]

(i)

Determine the frequency of $V_{I N}$ .
frequency = Hz

[ 1 ]

$\begin{aligned} \text { frequency } =1 / 0.04 =25 \mathrm{~Hz} \end{aligned}$

(d)

The circuit of Fig. 5.1 is modified so that it produces full-wave rectification of an input voltage. Suggest, with a reason, how $V_{\text {OUT }}$ now varies with time when $V_{\text {IN }}$ is as shown in Fig. 5.2.

[ 2 ]

$V_{\text {IN }}$ has constant magnitude in both positive and negative directions
(so) $V_{\text {out }}$ is (now) constant / $V_{\text {out }}$ does not vary with time

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

Question (iii)

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question (a)

Question (b)

Question (c)

Question (i)

Question (d)