CAIE A-Level Physics 21.1 Characteristics of Alternating Currents

Practise analysing sinusoidal current and voltage, period, frequency, peak and rms values, and calculating mean or instantaneous resistive power.

Exam points

analyse period, frequency, peak and rms values and use sinusoidal current or voltage equations
calculate mean and instantaneous power in a resistive load

Covered syllabus points

21.1.1—The terms period, frequency and peak value as applied to an alternating 21.1.2—Equations of the form x = x0 sin ωt representing a sinusoidally alternating 21.1.3—The fact that the mean power in a resistive load is half the maximum power 21.1.4—Root-mean-square (r.m.s.) and peak values and recall and use I r.m.s. = I0 /

[Maximum number: 1]

A bridge rectifier contains four diodes. The output of the rectifier is connected to a resistor R, as shown in Fig. 10.1.

Fig. 10.1

The variation with time t of the input e.m.f. E to the rectifier is given by the expression

E=15 \cos (210 t)

where t is measured in seconds and E in volts.
The variation with time t of the potential difference V across resistor R is shown in Fig. 10.2.

Fig. 10.2

Determine:

the maximum potential difference $V_{\text {MAX }}$ across resistor R

V_{\operatorname{MAX}}=

$V_{\text {MAX }}=15 \mathrm{~V}$

A1

[Maximum number: 2]

The output potential difference (p.d.) of an alternating power supply is represented by

V=320 \sin (100 \pi t)

where V is the p.d. in volts and t is the time in seconds.

(a)

Determine the root-mean-square (r.m.s.) p.d. of the power supply.

r.m.s. p.d. =

[ 1 ]

(b)

Determine the period T of the output.

[ 1 ]

$\omega=100 \pi$ $T=\frac{2 \pi}{\omega}=\frac{2 \pi}{100 \pi}$

C1

=0.020 s

A1

[Maximum number: 4]

(a)

The output voltage V of an a.c. power supply varies sinusoidally with time t as shown in Fig. 7.2.

Fig. 7.2

[ 4 ]

(i)

Determine the equation for V in terms of t, where V is in volts and t is in seconds.

[ 2 ]

$\begin{aligned} \omega =2 \pi / \top =2 \pi / 2.5 =0.80 \pi \text { or } 4 \pi / 5 \text { or } 2.5 \end{aligned}$

C1

$(V=) \mathbf{3 . 5} \sin (\mathbf{0 . 8} \pi \boldsymbol{t})$ or $3.5 \sin (4 \pi t / 5)$ or $3.5 \sin (2.5 t)$

A1

(ii)

The supply is connected to a $12 \Omega$ resistor. Calculate the mean power dissipated in the resistor.
mean power =
W

[ 2 ]

$(\mathrm{P}=) \frac{\mathrm{V}^{2}}{2 \mathrm{R}} \text { or }(\mathrm{P}=) \frac{V_{\text {r.m.s. }}{ }^{2}}{\mathrm{R}}$ $=\frac{3.5^{2}}{2 \times 12}$ or $\frac{2.47^{2}}{12}$

C1

$=0.51 \mathrm{~W}$

A1

All question bank results loaded

Covered syllabus points

21.1 Characteristics of alternating currents question 1

21.1 Characteristics of alternating currents question 2

Question (a)

Question (b)

21.1 Characteristics of alternating currents question 3

Question (a)

Question (i)

Question (ii)