Université Grenoble Alpes
2022/2023
PHY237
DC Electricity
Tutorials
Exercise 1 : Current, electron flow
1. How many electrons travel per second through the cross-section of a Copper wire, when the
current passing through the wire is 1.6 mA ?
2. A battery provides a current courant I = 1.5 A during a time t = 70 h. What is the total charge
provided during the same time ?
3. On a car battery, we can read 45 A.h / 200 A. What does it mean ? How long can the battery
deliver a 1A current ? What is the total charge Q that circulates in the circuit when we start the
engine (assuming that current is 120A and starting lasts 2s) ?
Exercise 2 : Lab wires
During the practicals you will use cables, 1m-long with a 1mm2 cross-section. They are made out
of Copper with ρ = 1.7 µΩ.cm.
1. What is the electrical resistance of such cables ?
2. During the practical sessions, the currents you will use are always smaller than 1 A (except if you
make a mistake : short-cuts !). In the worst case, what will be the error concerning the voltage
drop across a cable if you neglect it ?
Exercise 3 : Choosing cables for powering a house
We want to be able to handle 6 kW electrical power in a house. The main voltage is 220 V.
1. What is the required current ?
2. To minimize heating, one should keep the current density below 1A/mm2 . What is the required
cross-section for this house ?
3. If the cable is cylindrical, what is its radius ?
Exercise 4 : Integrated circuit conducting stripes
The components of a microprocessor are connected using Aluminum conducting stripes. Al resistivity is ρ = 3 µΩ.cm. We consider L = 20 µm stripes and the specification is that connections must be
less that 1 Ω resistive.
1. What should be the minimum cross-section for such connections ?
2. If the stripes are 1 µm wide, what should be their thickness e ?
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Université Grenoble Alpes
2022/2023
Exercise 5 : Series and Parallel combinations
For each circuit below :
1. Identify resistors connected together in series or parallel.
2. Reduce the combination to a single equivalent resistor.
Exercise 6 : Infinite loops
One adds up an infinite number of identical loops in a parallel combination.
1. Reduce the 1-loop combination to a single equivalent resistor (left figure).
2. Reduce the 2-loop combination to a single equivalent resistor (center figure).
3. Deduce the equivalent resistor for n-loop combination with n → ∞ (right figure).
Exercise 7 : Voltage divider
Apply a voltage divider to express U2 or U20 with circuit parameters.
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PHY237