A wire carries a current of \(5.6\,\mathrm{A}\).
What is the number of conduction electrons that pass a point on the wire in a time of \(20\,\mathrm{s}\)?
Correct Answer: \( \boxed{\mathrm{D}} \)
The charge passing the point is
\(Q=It=5.6\times20=112\,\mathrm{C}\).
The number of electrons is
\(n=\dfrac{Q}{e}=\dfrac{112}{1.60\times10^{-19}}\approx7.0\times10^{20}\).
Therefore, the correct answer is (D).
Two cylindrical conductors, \(X\) and \(Y\), are made from the same material. The conductors have equal lengths, but \(Y\) has a smaller diameter than \(X\).
\(X\) and \(Y\) are connected in series to a cell.
Which row compares the number of charge carriers per unit time passing through \(X\) and through \(Y\) and compares the average drift speed of the charge carriers in \(X\) and in \(Y\)?
| Number of charge carriers per unit time | Average drift speed of charge carriers | |
| (A) | Y greater than X | Y greater than X |
| (B) | Y same as X | Y same as X |
| (C) | Y greater than X | Y same as X |
| (D) | Y same as X | Y greater than X |
Correct Answer: \( \boxed{\mathrm{D}} \)
Since the conductors are connected in series, the same current flows through both. Therefore, the number of charge carriers passing a cross-section per unit time is the same.
The drift speed is given by
\(I=nAv_dq\).
As conductor \(Y\) has a smaller cross-sectional area, the drift speed must be greater to maintain the same current.
Therefore, the correct answer is (D).
A metal electrical conductor has a resistance of \(5.6\,\mathrm{k\Omega}\). A potential difference (p.d.) of \(9.0\,\mathrm{V}\) is applied across its ends.
How many electrons pass a point in the conductor in one minute?
Correct Answer: \( \boxed{\mathrm{C}} \)
The current is
\(I=\dfrac{V}{R}=\dfrac{9.0}{5.6\times10^3}=1.61\times10^{-3}\,\mathrm{A}\).
The charge passing in \(60\,\mathrm{s}\) is
\(Q=It=(1.61\times10^{-3})(60)=9.64\times10^{-2}\,\mathrm{C}\).
The number of electrons is
\(N=\dfrac{Q}{e}=\dfrac{9.64\times10^{-2}}{1.60\times10^{-19}}\approx6.0\times10^{17}\).
Therefore, the correct answer is (C).
