Exercise EE1-04.K1

Prof. Dr. Thorsten Jungmann (last updated 2025-12-07)

Relates to EE1-04 Resistance

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Task 1: Ohm’s law and fundamentals

Mark the correct statement(s):

a) The electric resistance is the ratio of voltage to current: $R=\frac{U}{I}$.

b) At constant resistance, the current is proportional to the applied voltage.

c) A conductance of 2 siemens corresponds to a resistance of 2 ohms.

d) Resistivity is a temperature-independent material constant.

Solution

a), b) are correct

Task 2: Temperature dependence

Mark the false statement(s):

a) The resistance of metals increases with rising temperature.

b) Semiconductors show PTC behaviour; their resistance decreases with rising temperature.

c) The temperature coefficient $\alpha$ is identical for all metals.

d) The formula $R(T)=R_{20}(1+{\alpha }_{20}\cdot \Delta T)$ applies approximately to small changes in temperature.

Solution

b), c) are false

Task 3: Electric circuits of resistors

Mark the correct statement(s):

a) In a series connection, the individual resistances add up to the total resistance.

b) The total resistance of a parallel connection is always smaller than the smallest individual resistance.

c) In a parallel connection, the voltage divides in the ratio of the resistances.

d) Two identical resistors connected in parallel result in half the resistance.

Solution

a), b), d) are correct

Task 4: Material properties

Match the materials (left) to their typical resistivities at $20°C$ (right):

Material		Resistivity
A) Copper		1) $10^{16}\mathrm{\Omega }\cdot \mathrm{m}{\mathrm{m}}^2/m$
B) Aluminium		2) $0.0178\mathrm{\Omega }\cdot \mathrm{m}{\mathrm{m}}^2/m$
C) Constantan		3) $0.0287\mathrm{\Omega }\cdot \mathrm{m}{\mathrm{m}}^2/m$
D) Silver		4) $0.50\mathrm{\Omega }\cdot \mathrm{m}{\mathrm{m}}^2/m$
E) PVC (insulator)		5) $0.016\mathrm{\Omega }\cdot \mathrm{m}{\mathrm{m}}^2/m$

Solution

A→2 (copper), B→3 (aluminium), C→4 (constantan), D→5 (silver), E→1 (PVC)

Task 5: Formulas and relationships

Match the formulas (left) to their application (right):

Formula		Application
A) $R=\rho \cdot \frac{l}{A}$		1) Total resistance of a series connection
B) $R(T)=R_{20}(1+{\alpha }_{20}\cdot \Delta T)$		2) Calculating the conductor resistance
C) $R_{\mathrm{tot}}={\sum }_{i=1}^n{R}_i$		3) Voltage divider
D) $G=\frac{1}{R}$		4) Temperature dependence
E) $\frac{I_1}{I_2}=\frac{R_2}{R_1}$		5) Parallel connection of two resistors
		6) Current divider
		7) Power in a resistor
		8) Conductance from resistance

Solution

A→2, B→4, C→1, D→8, E→6

Task 6: Resistor colour code

Match the colour bands (left) to the correct resistances (right):

Colour bands		Resistance
A) brown – black – red – gold		1) $47\mathrm{\Omega }\pm 5\%$
B) yellow – violet – black – gold		2) $1.0\mathrm{k\Omega }\pm 5\%$
C) red – red – orange – silver		3) $470\mathrm{\Omega }\pm 5\%$
D) orange – orange – brown – gold		4) $22\mathrm{k\Omega }\pm 10\%$
E) green – blue – brown – silver		5) $330\mathrm{\Omega }\pm 5\%$
		6) $560\mathrm{\Omega }\pm 10\%$
		7) $10\mathrm{k\Omega }\pm 5\%$

Solution

A→2 ($1.0\mathrm{k\Omega }$), B→1 ($47\mathrm{\Omega }$), C→4 ($22\mathrm{k\Omega }$), D→5 ($330\mathrm{\Omega }$), E→6 ($560\mathrm{\Omega }$)