Current Electricity flash cards

1. 1.Define electric current. Is it a scalar or a vector?

   Electric current is the rate of flow of charge: $I=\dfrac{q}{t}$ (or $I=\dfrac{dq}{dt}$). It is a scalar quantity, though it has direction, because it does not obey the laws of vector addition (it follows algebraic addition at a junction).

   Hint: Charge per unit time; scalar despite having direction.

2. 2.What is the SI unit of current and how is $1$ ampere defined in terms of charge?

   The SI unit is the ampere (A). $1$ A means $1$ coulomb of charge flowing per second: $1\text{ A}=1\text{ C/s}$.

   Hint: Coulomb per second.

3. 3.What is conventional current and how does its direction relate to electron flow?

   Conventional current is taken in the direction of flow of positive charge. In a metallic conductor, electrons (negative) actually move opposite to the conventional current direction.

   Hint: Conventional = direction of positive charge = opposite to electrons.

4. 4.What are the charge carriers in metals, electrolytes, and semiconductors?

   Metals: free electrons. Electrolytes: positive and negative ions. Semiconductors: electrons and holes.

   Hint: Electrons / ions / electrons+holes.

5. 5.Define drift velocity of electrons in a conductor.

   Drift velocity is the small average velocity ($\sim 10^{-4}$ m/s) with which free electrons drift opposite to the applied electric field, superimposed on their random thermal motion.

   Hint: Average net velocity due to the field.

6. 6.State the relation between current and drift velocity.

   $I=neAv_d$, where $n$ = number density of electrons, $e$ = electronic charge, $A$ = cross-sectional area, $v_d$ = drift velocity.

   Hint: $I=neAv_d$.

7. 7.How is drift velocity related to the applied electric field and relaxation time?

   $v_d=\dfrac{eE}{m}\tau$, where $\tau$ is the relaxation time (average time between successive collisions) and $E$ is the electric field.

   Hint: $v_d=eE\tau/m$.

8. 8.Define relaxation time $\tau$.

   Relaxation time is the average time interval between two successive collisions of an electron with the ions/atoms of the conductor lattice. Typically $\tau\sim 10^{-14}$ s.

   Hint: Average time between collisions.

9. 9.Define current density $\vec{j}$ and give its SI unit.

   Current density is current per unit cross-sectional area (normal to flow): $j=\dfrac{I}{A}$. It is a vector in the direction of current flow. SI unit: $\text{A/m}^2$.

   Hint: $j=I/A$, vector, A m$^{-2}$.

10. 10.Write current density in terms of drift velocity, and its vector form.

    $j=nev_d$, and in vector form $\vec{j}=ne\vec{v}_d$ (pointing along conventional current, opposite to $\vec{v}_d$ of electrons).

    Hint: $j=nev_d$.

11. 11.State Ohm's law and the condition under which it holds.

    Ohm's law: at constant temperature, the current through a conductor is directly proportional to the potential difference across it, $V\propto I$, i.e. $V=IR$. It holds only when physical conditions (especially temperature) remain constant.

    Hint: $V=IR$ at constant temperature.

12. 12.Define electrical resistance and give its SI unit.

    Resistance is the opposition offered by a conductor to the flow of current: $R=\dfrac{V}{I}$. SI unit: ohm ($\Omega$), where $1\ \Omega = 1$ V/A.

    Hint: $R=V/I$; unit ohm.

13. 13.How does resistance of a wire depend on its length and area of cross-section?

    $R=\rho\dfrac{L}{A}$: resistance is directly proportional to length $L$ and inversely proportional to area $A$, where $\rho$ is resistivity.

    Hint: $R=\rho L/A$.

14. 14.Define resistivity (specific resistance) and give its SI unit.

    Resistivity $\rho$ is the resistance of a conductor of unit length and unit cross-sectional area: $\rho=\dfrac{RA}{L}$. SI unit: ohm-metre ($\Omega\,\text{m}$). It depends on material and temperature, not on dimensions.

    Hint: $\rho=RA/L$; unit $\Omega$ m.

15. 15.Define electrical conductivity and conductance with their units.

    Conductivity $\sigma=\dfrac{1}{\rho}$ (unit $\Omega^{-1}\text{m}^{-1}$ or S/m). Conductance $G=\dfrac{1}{R}$ (unit siemens, S or $\Omega^{-1}$).

    Hint: Reciprocals of resistivity and resistance.

16. 16.Write the microscopic (vector) form of Ohm's law.

    $\vec{j}=\sigma\vec{E}$, i.e. current density is proportional to electric field, where $\sigma$ is the conductivity. Equivalently $\vec{E}=\rho\vec{j}$.

    Hint: $j=\sigma E$.

17. 17.Express resistivity in terms of electron number density and relaxation time.

    $\rho=\dfrac{m}{ne^2\tau}$, where $m$ = electron mass, $n$ = number density, $e$ = charge, $\tau$ = relaxation time. Conductivity $\sigma=\dfrac{ne^2\tau}{m}$.

    Hint: $\rho=m/(ne^2\tau)$.

18. 18.What is a mobility of charge carriers? Give its SI unit.

    Mobility $\mu$ is the drift velocity per unit electric field: $\mu=\dfrac{v_d}{E}=\dfrac{e\tau}{m}$. SI unit: $\text{m}^2\,\text{V}^{-1}\text{s}^{-1}$.

    Hint: $\mu=v_d/E$.

19. 19.What are ohmic and non-ohmic conductors? Give one example of each.

    Ohmic conductors obey Ohm's law (linear $V$–$I$ graph), e.g. a metallic wire. Non-ohmic conductors do not (non-linear $V$–$I$ graph), e.g. a diode, filament bulb, or thyristor.

    Hint: Linear vs non-linear V–I graph.

20. 20.For an ohmic conductor, what does the slope of the $V$ versus $I$ graph give?

    The slope of a $V$ (y-axis) versus $I$ (x-axis) straight-line graph gives the resistance $R$. A steeper slope means larger resistance.

    Hint: Slope of V–I = R.

21. 21.How does the resistance of a metallic conductor change with temperature, and why?

    Resistance increases with temperature. As temperature rises, ions vibrate more, decreasing relaxation time $\tau$, so resistivity and hence resistance increase.

    Hint: Increases; $\tau$ decreases.

22. 22.Define temperature coefficient of resistance $\alpha$ and write $R_T$ in terms of it.

    $\alpha=\dfrac{R_T-R_0}{R_0\,\Delta T}$, giving $R_T=R_0(1+\alpha\Delta T)$. SI unit of $\alpha$: $\text{K}^{-1}$ or $^\circ\text{C}^{-1}$. For metals $\alpha$ is positive.

    Hint: $R_T=R_0(1+\alpha\Delta T)$.

23. 23.How does resistivity of semiconductors vary with temperature? What is the sign of $\alpha$?

    For semiconductors, resistivity decreases with rising temperature (more charge carriers are freed), so $\alpha$ is negative.

    Hint: Decreases; negative $\alpha$.

24. 24.Why do alloys like manganin and constantan have low temperature coefficients of resistance?

    Alloys such as manganin and constantan have very small $\alpha$, so their resistance is nearly independent of temperature. This makes them ideal for standard resistors and resistance wires.

    Hint: Nearly temperature-independent resistance.

25. 25.How does resistivity depend on temperature? Compare conductors, alloys, and semiconductors.

    Conductors: $\rho$ increases roughly linearly with $T$. Alloys: $\rho$ increases very slowly (small $\alpha$). Semiconductors and insulators: $\rho$ decreases with $T$.

    Hint: Up (metals), slightly up (alloys), down (semiconductors).

26. 26.When resistors are connected in series, what is the equivalent resistance and what is common to all?

    $R_s=R_1+R_2+R_3+\dots$ The same current flows through each, while the voltage divides. $R_s$ is greater than the largest individual resistance.

    Hint: Add them; same current.

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