Physics tutorial #16
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1. A copper wire has a diameter of 1.0 mm and at a temperature of 20 C carries a constant current of
1.67 A to a 200-watt lamp. The density of free electrons is 8.5 × 1028 electrons per cubic meter. Find
the magnitudes of (a) the current density, (b) the drift velocity, (c) the electric field in the wire if we
know that ÁCu = 1.72 × 10-8 &!·m, (d) the potential difference between two points in the wire 50.0 m
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apart, (e) the resistance of a 50.0-m length of this wire, and (f) its resistance at 0 C and 100 C.
2. A hollow cylinder has length L and inner and outer radii a and b. It is made of a material with
resistivity Á. A potential difference is set up between the inner and outer surfaces of the cylinder
(each of which is an equipotential surface) so that current flows radially through the cylinder. What
is the resistance to this radial current flow? (Hint: ...dr)
3. (a) Fig. 1 shows a source (a battery) with an emf E of 12 V and an internal resistance r of 2 &!. The
wires to the left of the battery and to the right of the ammeter A are not connected to anything.
Determine the readings of the idealised voltmeter V and ammeter A. (b) We add a 4-&! resistor R
to form the complete circuit shown in Fig. 2. What are the voltmeter and ammeter readings now?
(c) Using the same battery, we now replace the 4-&! resistor with a zero-resistance conductor. What
are the meter readings now?
V V
r µ r µ
A A
R
Fig. 1 Fig. 2
4. (a) A 12-V car battery with negligible internal resistance provides the starting current of 300 A. Find
the resistance of the starter and the available starting power. (b) Battery terminals, particularly
the positive terminal, tend to accumulate corrosion which may contribute to electrical resistance at
the terminal. How would the values of the current from the battery, the total power and the power
available to the starter, be changed if there was a terminal resistance of 0.1 ohms?
5. A source with emf E and internal resistance r is connected to an external circuit. (a) Show that the
power output of the source is maximum when the current in the circuit is one-half the short-circuit
current of the source. (b) If the external circuit consists of a resistance R, show that the power
output is maximum when R = r and that the maximum power is E2/4r.
6. A resistor with resistance 10 M&! is connected in series with a capacitor with capacitance 1.0 µF and
a battery with emf 12.0 V. Before the switch is closed at time t = 0, the capacitor is uncharged.
(a) What is the time constant? (b) What fraction of the final charge is on the plates at time t = 46 s?
(c) What fraction of the initial current remains at t = 46 s?
7. Fig. 3 shows a  bridge circuit with an emf E of 13 V and R equal 1 &!. Find the current in each
resistor and the equivalent resistance of the network of five resistors.
R R
R
µ
R 2R
Fig. 4
Fig. 3
8. Each of the three resistors in Fig. 4 has a resistance of 2.4 &! and can dissipate a maximum of 36 W
without becoming excessively heated. What is the maximum power the circuit can dissipate? Is it
possible to connect the resistors in some other way to increase the maximum power?
Nivas Babu Selvaraj, Maciej Woloszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/