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Institutt for fysikk, NTNU

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TFY4155/FY1003: Elektrisitet og magnetisme

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V{\aa}r 2005

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{\O}ving 11
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Guidance: Thursday March 31 and Friday April 1

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To be delivered by: Monday April 4

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{\em Exercise 1}

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The figure below shows an electric circuit with 5 resistors $R_j$, $j = 1,..,5$.

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$a)$ Determine the total resistance $R$ between the points A and B, i.e.:
Determine the resistance $R$ in the equivalent circuit in the following figure:

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$b)$ An ideal voltage source with electromotive force $\cal E$ is connected
to the circuit so that $\Delta V = V_A - V_B = {\cal E}$. Determine the
resulting currents $I_j$ through each of the resistors $R_j$.

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(Unless otherwise specified, we always assume, in exercises like this one, that
the connecting wires between the various resistors are {\em perfect
conductors}, i.e., with zero resistance.)

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$c)$ Determine numerical values for $I_j$ when ${\cal E} = 9$ V and $R_j = j \; \Omega$.

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[A couple of answers: $I_1 = 0.89$ A, $I_5 = 1.62$ A]


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{\em Exercise 2}

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\noindent
Three identical light bulbs 1, 2 and 3 are put together in three different
circuits A, B and C, as shown in the figure. The light bulbs can be viewed as
identical ohmic resistors. Increased current implies increased power, and
hence increased light intensity.
The voltage source has the same emf $V_0$ in each of the three circuits.

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$a)$ Compare the light intensity in bulb nr 1 in the three circuits.
In which circuit is the intensity strongest, and where is it weakest?

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$b)$ What happens to the light in bulb nr 1 in each of the three circuits
if bulb nr 3 is removed?

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Explain your reasoning.

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\noindent
{\em Exercise 3}

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\noindent
The circuit in the figure is supposed to be used to measure how fast a physics
student is running. Before the student starts running,
there is a constant current in the circuit. The voltage source is
$V_0 = 9.00$ kV, the resistance $R = 1.00$ M$\Omega$, and the capacitance
$C = 150$ nF. The distance $d$ is 100 cm. The student cuts the circuit,
first in the position A, then in the position B. Now, the volt meter $V$ displays
a potential difference of 3.58 kV between the capacitor plates. How fast is the student
running?

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(An ideal volt meter simply measures the potential difference between two points
in a circuit without influencing the circuit in any way.
For example, no current runs through an ideal volt meter.)

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[Answer: ca 26 km/h]


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