Alternating Current

electric current, I = Anvq
resistors in series, R = R1 + R2+……….

1 1 1
resistors in parallel, = ........
R R1 R 2
Q
electric potential, V =
4SH o r
alternating current/voltage, x = xo sin Z t
1. The variation with time t of the voltage V of an alternating source applied across a 2.0 Ω
resistor is shown below.
V/V
4.0
t / ms
0
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
– 1.0
What is the power dissipated in the resistor?
A 0.98 W B 1.5 W C 1.9 W D 2.4 W
2. The variation with time of an alternating current Ip connected to the primary coil of a
transformer is as shown.
Ip
0
time
Which graph represents the variation with time of the power output, P, in a resistor
connected across the secondary coil?
A B
P P
time
0 0
time
3. A 1:12 step-up ideal transformer is connect to a light bulb. The resistor dissipates heat at a
rate of 36 W when the peak alternating voltage of the supply is 2.8 V.
supply resistor
The peak alternating voltage of the supply is then changed to 1.4 V.
What is the root-mean-square current in the primary coil?
A 6.4 A B 9.1 A C 26 A D 36 A
4. An alternating voltage of 230 kV is supplied to a transformer, which steps the voltage down to a
number of streetlamps with a rating of 230 V 150 W. If the maximum allowable current through
the primary coil is 10 A, what is the maximum number of streetlamps that can be connected in
parallel?
A 1500 B 6500 C 10000 D 15000
5. When an alternating power supply of 240 V r.m.s. is connected across PQ in the circuit shown
below.
The fuse F breaks the circuit if the current in it just exceeds 13 A r.m.s.
When the alternating power supply is replaced with a 120 V d.c. source, an identical fuse breaks
the circuit if the current just exceeds
13 13
A A B A C 13 A D 26 A
2 √2
6. An alternating power supply of root-mean-square voltage 4.0 V is connected across a resistive
load such that the average power dissipated across it is P.
What is the d.c. voltage applied across the same load which will give rise to an average power
dissipation of 3P ?
A 6.9 V B 8.5 V C 12 V D 17 V
7.
8.
9.
10.
STRUCTURE QUESTIONS
1. (a) State Lenz’s law.
………………………………………………………………………………………….
………………………………………………………………………………………….
…………………………………………………………………………………………. [1]
(b) A pair of parallel metal rails of negligible resistance are placed 12 cm apart in an
uniform magnetic field of strength 0.65 T applied perpendicularly to the rails out of
paper, as shown in Fig. 7.1. Two 15 cm long metal rods, AB and CD, are placed on
top of the rails and can slide smoothly along the rails. Rod AB has an electrical
resistance of 8.0 : while rod CD has an electrical resistance of 10 :. Rod AB is
pulled to the left by an external force at a constant speed of 2.0 m s–1 while rod CD
is pulled to the right at a constant speed of 3.0 m s–1.
A C
2.0 m s–1 15 cm 12 cm 3.0 m s–1
B D
Magnetic field of strength 0.65 T pointing out of paper
Fig. 1.1
(i) State which end of rods AB and CD has a higher potential.
Rod AB: ……….
Rod CD: ………. [2]

(ii) Determine the induced e.m.f. across each rod.
e.m.f. of rod AB = …………………. V

e.m.f. of rod CD = …………………. V [2]
(iii) Determine the induced current flowing in the rods.
induced current = …………………. A [2]
(iv) Hence calculate the total power dissipated in both rods.
total power = …………………. W [2]

(v) By considering your answer in (iv), show that energy is conserved during
this induction process.
…………………………………………………………………………………
…………………………………………………………………………………
………………………………………………………………………………… [3]
(c) State what is meant by root-mean-square current.
………………………………………………………………………………………….
………………………………………………………………………………………….
…………………………………………………………………………………………. [1]
(d) An ideal transformer is used to step up an alternating voltage Vin as shown in

Fig. 7.2. The secondary coil of the transformer is connected to a resistor of 4.0 :.
10 200
Vin turns turns 4.0 :
Fig. 1.2
Fig. 7.3 shows the variation of the power input at the primary coil with respect to
time t.
Pin / W
1.8
2 4 6 8 10 12
t / ms
60 120 180 240 300 360
Fig. 1.3
(i) Determine the root-mean-square voltage in the secondary coil.
root-mean-square voltage = …………………. V [2]
(ii) Determine the root-mean-square current flowing in the primary coil.
root-mean-square current = …………………. A [2]

(iii) Sketch the variation of input current Iin at the primary coil with respect [2]
to time t, in Fig. 1.4 and indicate the value of peak input current.
Iin / A
60 120 180 240 300 360 t / ms
Fig. 1.4
(iv) State the equation showing how input current Iin varies with time t.
…………………………………………………………………………………
………………………………………………………………………………… [1]

Alternating Current

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Alternating Current

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electric current, I = Anvq

resistors in series, R = R1 + R2+……….

What is the power dissipated in the resistor?

A 0.98 W B 1.5 W C 1.9 W D 2.4 W

The peak alternating voltage of the supply is then changed to 1.4 V.

What is the root-mean-square current in the primary coil?

A 1500 B 6500 C 10000 D 15000

1. (a) State Lenz’s law.

2.0 m s–1 15 cm 12 cm 3.0 m s–1

Magnetic field of strength 0.65 T pointing out of paper

(i) State which end of rods AB and CD has a higher potential.

Rod AB: ……….

Rod CD: ………. [2]

e.m.f. of rod AB = …………………. V

(iii) Determine the induced current flowing in the rods.

induced current = …………………. A [2]

(iv) Hence calculate the total power dissipated in both rods.

total power = …………………. W [2]

(c) State what is meant by root-mean-square current.

(d) An ideal transformer is used to step up an alternating voltage Vin as shown in

(i) Determine the root-mean-square voltage in the secondary coil.

root-mean-square voltage = …………………. V [2]

(ii) Determine the root-mean-square current flowing in the primary coil.

root-mean-square current = …………………. A [2]

60 120 180 240 300 360 t / ms

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