Q. No.A cylindrical conductor of length \(2~\text{m}\) and area of cross-section \(0.2 ~\text{mm}^2\) carries an electric current of \(1.6~\text {A}\) when its ends are connected to a \(2~\text {V}\) battery. Mobility of electrons in the conductor is \(\alpha \times 10^{-3} ~\text{m}^2 /\text{V.s}\). The value of \(\alpha\) is:
(electron concentration = \(5 \times 10^{23} / \text{m}^3\) and electron charge \(\left.=1.6 \times 10^{-19} ~\text{C}\right)\)
1. \(2\)
2. \(3\)
3. \(1\)
4. \(5\)
(electron concentration = \(5 \times 10^{23} / \text{m}^3\) and electron charge \(\left.=1.6 \times 10^{-19} ~\text{C}\right)\)
1. \(2\)
2. \(3\)
3. \(1\)
4. \(5\)
Subtopic: Current & Current Density |
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Current passing through a wire as function of time is given as \(I(t)=0.02t+0.01 ~\text{A}. \) The charge that will flow through the wire from \(t = 1 ~\text{s} \) to \(t = 2 ~\text{s} \) is:
1. \(0.06~\text{C}\)
2. \(0.04~\text{C}\)
3. \(0.02~\text{C}\)
4. \(0.07~\text{C}\)
1. \(0.06~\text{C}\)
2. \(0.04~\text{C}\)
3. \(0.02~\text{C}\)
4. \(0.07~\text{C}\)
Subtopic: Current & Current Density |
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If electric current passing through a conductor varies with time as \(I=I_0+\beta t\) where \(I_0=20~\text{A}, \beta=3~\text{A/s},\) then the charge flows through the conductor in the first \(10\) sec is:
1. \(400~\text{C}\)
2. \(500~\text{C}\)
3. \(200~\text{C}\)
4. \(350~\text{C}\)
1. \(400~\text{C}\)
2. \(500~\text{C}\)
3. \(200~\text{C}\)
4. \(350~\text{C}\)
Subtopic: Current & Current Density |
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The current through a conductor varies with time as \(i=3t^2+4t^3.\) Then the amount of charge (in \(\text{C}\) ) passes through the cross-section of a conductor in the interval \(t=1~\text{sec to}\) \(t=2~\text{sec}\) is:
1. \(28~\text C\)
2. \(32~\text C\)
3. \(48~\text C\)
4. \(22~\text C\)
1. \(28~\text C\)
2. \(32~\text C\)
3. \(48~\text C\)
4. \(22~\text C\)
Subtopic: Current & Current Density |
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When an electric field is applied to a conductor, in which direction do the electrons drift?
| 1. | In a straight line. |
| 2. | From higher potential to lower potential. |
| 3. | From lower potential to higher potential. |
| 4. | With constant velocity. |
Subtopic: Current & Current Density |
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A conductor of length \(l\) and cross-sectional are \(A\) has drift velocity \(v_d\) when used across a potential difference \(V\).
When another conductor of the same material and length \(l\) but double cross-sectional area than the first, is used across
the same potential difference then drift velocity is equal to:
1. \(\frac{v_d}{2}\)
2. \(v_d\)
4. \(2v_d\)
4. \(4v_d\)
When another conductor of the same material and length \(l\) but double cross-sectional area than the first, is used across
the same potential difference then drift velocity is equal to:
1. \(\frac{v_d}{2}\)
2. \(v_d\)
4. \(2v_d\)
4. \(4v_d\)
Subtopic: Current & Current Density |
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If \(n:\) number density of charge carriers.
\(A:\) cross-sectional area of the conductor
\(q:\) charge on each charge carrier
\(I:\) current through the conductor
Then the expression of drift velocity is:
1. \(\frac{nAq}{I}\)
2. \(\frac{I}{nAq}\)
3. \({nAqI}\)
4. \(\frac{IA}{nq}\)
\(A:\) cross-sectional area of the conductor
\(q:\) charge on each charge carrier
\(I:\) current through the conductor
Then the expression of drift velocity is:
1. \(\frac{nAq}{I}\)
2. \(\frac{I}{nAq}\)
3. \({nAqI}\)
4. \(\frac{IA}{nq}\)
Subtopic: Current & Current Density |
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The current density in a cylindrical wire of radius \(r= 4.0~\text{mm}\) is \(1.0 \times 10^6 ~\text{A/m}^2\). The current through the outer portion of the wire between radial distances \(\frac{r}{2}\) and \(r\) is \(x\pi~ \text{A}\), where \(x\) is:
1. \(10\)
2. \(14\)
3. \(16\)
4. \(12\)
1. \(10\)
2. \(14\)
3. \(16\)
4. \(12\)
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A cylindrical wire of radius \(4~\text{mm} \) carries a uniform current density of \(4 \times 10^6~ \text{Am}^{-2}.\) What is the current flowing through the outer portion of the wire between radial distances \(\dfrac{R}{2}\) and \(R \text{?}\)
| 1. | \(16\pi~\text{A}\) | 2. | \(64\pi~\text{A}\) |
| 3. | \(32\pi~\text{A}\) | 4. | \(48\pi~\text{A}\) |
Subtopic: Current & Current Density |
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Consider the following statements regarding the drift velocity of electrons in a conductor:
Choose the correct answer from the options given below:
| (A) | The drift velocity of electrons decreases with an increase in the temperature of the conductor. |
| (B) | The drift velocity is inversely proportional to the cross-sectional area of the conductor. |
| (C) | The drift velocity is independent of the applied potential difference across the conductor. |
| (D) | The drift velocity is inversely proportional to the length of the conductor. |
| (E) | The drift velocity increases with an increase in the temperature of the conductor. |
Choose the correct answer from the options given below:
| 1. | (A) and (B) only |
| 2. | (A) and (D) only |
| 3. | (B) and (E) only |
| 4. | (B) and (C) only |
Subtopic: Current & Current Density |
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