CAPÍTULO 3: NIVELES COMUNES DE REFERENCIA
3.5. La flexibilidad de un enfoque ramificado
1 The internal resistance of a dry cell increases gradually with age, even if the cell is not being used. However, the e.m.f. remains approximately constant. You can check the age of a cell by connecting a low-resistance ammeter across the cell and measuring the current. For a new 1.5 V cell of a certain type, the short-circuit current should be about 30 A.
a Calculate the internal resistance of a new cell.
b A student carries out this test on an older cell, and finds the short-circuit current to be only 5 A. Calculate the internal resistance of this cell.
2 A torch bulb has a power supply of two 1.5 V cells connected in series. The potential difference across the bulb is 2.2 V, and it dissipates energy at the rate of 550 mW. Calculate:
a the current through the bulb, b the internal resistance of each cell,
c the heat energy dissipated in each cell in two minutes.
3 Two identical light bulbs are connected first in series, and then in parallel, across the same battery (assumed to have negligible internal resistance). Use Kirchhoff’s laws to decide which of these connections will give the greater total light output.
4 You are given three resistors of resistance 22 Ω, 47 Ω and 100 Ω. Calculate:
a the maximum possible resistance, b the minimum possible resistance,
that can be obtained by combining any or all of these resistors.
5 In the circuit of Fig. 20.25, the currents I1 and I2 are equal.
Calculate:
a the resistance R of the unknown resistor, b the total current I3.
6 Fig. 20.26 shows a potential divider circuit, designed to provide p.d.s of 1.0 V and 4.0 V from a battery of e.m.f.
9.0 V and negligible internal resistance.
a Calculate the value of resistance R.
b State and explain what happens to the voltage at terminal A when an additional 1.0 Ω resistor is connected between terminals B and C in parallel with the 5.0 Ω resistor. No calculations are required.
15 Ω
7 A student designs an electrical method to monitor the position of a steel sphere rolling on two parallel rails. Each rail is made from bare wire of length 30 cm and resistance 20 Ω. The position-sensing circuit is shown in Fig. 20.27.
The resistance of the steel sphere and the internal resistance of the battery are negligible.
resistance wire
a State the voltage across the 10 Ω resistor when the sphere is at A, where l = 0.
b With the sphere at end B of the rails, calculate:
i the total resistance of the circuit, ii the current in the 10 Ω resistor, iii the output voltage V.
8 Two equations for the power P dissipated in a resistor are P = I2R and P = V2/R. The first suggests that the greater the resistance R of the resistor, the more power is dissipated. The second suggests the opposite: the greater the resistance, the less the power. Explain this inconsistency.
9 State the minimum number of resistors, each of the same resistance and power rating of 0.5 W, which must be used to produce an equivalent 1.2 kΩ, 5 W resistor. Calculate the resistance of each, and state how they should be connected.
10 In the circuit shown in Fig. 20.28 the current in the battery is 1.5 A. The battery has internal resistance 1.0 Ω.
Calculate:
a the combined resistance of the resistors that are connected in parallel in the circuit of Fig. 20.28, b the total resistance of the circuit,
c the resistance of resistor Y,
d the current through the 6 Ω resistor.
Exam style questions
20 D.C. circuits
starting the engine. The connecting cable has total length 1.3 m, and consists of 15 strands of wire, each of diameter 1.2 mm. The resistivity of the metal of the strands is 1.4 × 10−8 Ω m.a Calculate:
i the resistance of each strand, ii the total resistance of the cable, iii the power loss in the cable.
b When the starter motor is used to start the car, 700 C of charge pass through a given cross-section of the cable.
i Assuming that the current is constant at 160 A, calculate for how long the charge flows.
ii Calculate the number of electrons which pass a given cross-section of the cable in this time. The electron charge e is −1.6 × 10−19 C.
c The e.m.f. of the battery is 13.6 V and its internal resistance is 0.012 Ω. Calculate:
i the potential difference across the battery terminals when the current in the battery is 160 A,
ii the rate of production of heat energy in the battery.
12 A copper wire of length 16 m has a resistance of 0.85 Ω.
The wire is connected across the terminals of a battery of e.m.f. 1.5 V and internal resistance 0.40 Ω.
a Calculate the potential difference across the wire and the power dissipated in it.
b In an experiment, the length of this wire connected across the terminals of the battery is gradually reduced.
i Sketch a graph to show how the power dissipated in the wire varies with the connected length.
ii Calculate the length of the wire when the power dissipated in the wire is a maximum.
iii Calculate the maximum power dissipated in the wire.
13 a i State Kirchhoff’s second law. [1]
ii Kirchhoff’s second law is linked to the conservation of a certain quantity.
State this quantity. [1]
b The circuit shown in Fig. 20.29 is used to compare potential differences.
The uniform resistance wire XY has length 1.00 m and resistance 4.0 Ω. Cell A has e.m.f. 2.0 V and internal resistance 0.50 Ω. The current through cell A is I. Cell B has e.m.f. E and internal resistance r.
The current through cell B is made zero when the movable connection J is adjusted so that the length of XJ is 0.90 m. The variable resistor R has resistance 2.5 Ω.
i Apply Kirchhoff’s second law to the circuit
CXYDC to determine the current I. [2]
ii Calculate the potential difference across the
length of wire XJ. [2]
iii Use your answer in ii to state the value of E. [1]
iv State why the value of the internal resistance of cell B is not required for the determination
of E. [1]
Cambridge International AS and A level Physics 9702/21 May/June 2012 14 A thermistor has resistance 3900 Ω at 0°C and resistance
1250 Ω at 30°C. The thermistor is connected into the circuit of Fig. 20.30 in order to monitor temperature changes.
R V 1.50 V
thermistor
Fig. 20.30
The battery of e.m.f. 1.50 V has negligible internal resistance and the voltmeter has infinite resistance.
a The voltmeter is to read 1.00 V at 0°C. Show that the resistance of resistor R is 7800 Ω. [2]
b The temperature of the thermistor is increased to 30°C.
Determine the reading on the voltmeter. [2]
c The voltmeter in Fig. 20.30 is replaced with one having a resistance of 7800 Ω. Calculate the reading on this voltmeter for the thermistor at a temperature of 0°C. [2]
Cambridge International AS and A level Physics, 9702/02 May/June 2004 Q 8 15 A car battery has an internal resistance of 0.060 Ω. It is
re-charged using a battery charger having an e.m.f. of 14 V and an internal resistance of 0.10 Ω, as shown in Fig. 20.31.
a At the beginning of the re-charging process, the current in the circuit is 42 A and the e.m.f. of the battery is E (measured in volts).
i For the circuit of Fig. 20.31, state 1 the magnitude of the total resistance,
2 the total e.m.f. in the circuit. Give your answer in
terms of E. [2]
ii Use your answers to i and data from the question to determine the e.m.f. of the car battery at the beginning of the re-charging process. [2]
b For the majority of the charging time of the car battery, the e.m.f. of the car battery is 12 V and the charging current is 12.5 A. The battery is charged at this current for 4.0 hours. Calculate, for this charging time,
i the charge that passes through the battery, [2]
ii the energy supplied from the battery charger, [2]
iii the total energy dissipated in the internal resistance of the battery charger and the car battery. [2]
c Use your answers in b to calculate the percentage efficiency of transfer of energy from the battery charger to stored energy in the car battery. [2]
Cambridge International AS and A level Physics, 9702/02 May/June 2007 Q 6
16 A circuit used to measure the power transfer from a battery is shown in Fig. 20.32. The power is transferred to a variable resistor of resistance R.
• •
The battery has an electromotive force (e.m.f.) E and an internal resistance r. There is a potential difference (p.d.) V across R. The current in the circuit is I.
a By reference to the circuit shown in Fig. 20.32, distinguish between the definitions of e.m.f.
and p.d. [3]
b Using Kirchoff’s second law, determine an expression for the current I in the circuit. [1]
c The variation with current I of the p.d. V across R is
ii the internal resistance r. [2]
d i Using the data from Fig. 20.33, calculate the power transferred to R for a current of 1.6 A. [2]
ii Use your answers from c i and d i to calculate the efficiency of the battery for a current of 1.6 A. [2]
Cambridge International AS and A Level Physics, 9702/23 Oct/Nov 2012 Q 4
Exam style questions
26 Particle physics
AS Level
Starting points
● The atom consists of a very small nucleus containing protons and neutrons, surrounded by orbiting electrons.
● The decay of unstable nuclei leads to emissions.
● Appreciate that protons and neutrons are not fundamental particles.
26.1 Atomic structure and radioactivity
The atoms of all elements are made up of three particles called protons, neutrons, and electrons. The protons and neutrons are at the centre or nucleus of the atom.
The electrons orbit the nucleus.
We shall see later that the diameter of the nucleus is only about 1/10 000 of the diameter of an atom.
Figure 26.1 illustrates very simple models of a helium atom and a lithium atom.
The protons and neutrons both have a mass of about one atomic mass unit u (1 u = 1.66 × 10−27 kg). The atomic mass unit is defined and used in the A level course in Topic 10. By comparison, the mass of an electron is very small, about 1/2000 of 1 u. The vast majority of the mass of the atom is therefore in the nucleus.
By the end of this topic, you will be able to:
26.1 (a) infer from the results of the α-particle scattering experiment the existence and small size of the nucleus
(b) describe a simple model for the nuclear atom to include protons, neutrons and orbital electrons (c) distinguish between nucleon number and proton
number
(d) understand that an element can exist in various isotopic forms, each with a different number of neutrons
(e) use the usual notation for the representation of nuclides
(f) appreciate that nucleon number, proton number and mass-energy are all conserved in nuclear processes
(g) show an understanding of the nature and properties of α-, β- and γ-radiations (both β− and β+ are included)
(h) state that (electron) antineutrinos and (electron) neutrinos are produced during β− and β+ decay 26.2 (a) appreciate that protons and neutrons are not
fundamental particles since they contain quarks (b) describe a simple quark model of hadrons in
terms of up, down and strange quarks and their respective antiquarks
(c) describe protons and neutrons in terms of a simple quark model
(d) appreciate that there is a weak interaction between quarks, giving rise to β decay (e) describe β− and β+ decay in terms of a simple
quark model
(f) appreciate that electrons and neutrinos are leptons
26.1 Atomic structure and radioactivity
26 Particle physics
The basic properties of the proton, neutron and electron are summarised in Table 26.1.
neutrons and protons form the nucleus of an atom
electrons orbit the nucleus
electrons carry a negative charge of 1e where e 1.6 10 19
protons carry a positive charge of 1e
C
neutrons carry no charge
a) b)
Figure 26.1 Structures of a) a helium atom and b) a lithium atom Table 26.1
approximate
mass charge position
proton u +e in nucleus
neutron u 0 in nucleus
electron u/2000 −e orbiting nucleus