The Flow of Electrons as Electric Current

Q. A beam of electrons moving at a speed of ${10}^6$ m/s along a line produces a current of $1.6\times {10}^{-6}A$. The number of electrons in the 1 metre of the beam is

1. ${10}^6$
2. ${10}^7$
3. ${10}^{13}$
4. ${10}^{19}$

Q. The belt of an electrostatic generator is $50cm$ wide and travels $30cm/s$. The belt carries charge into the sphere at a rate corresponding to ${10}^{-4}A$. What is the surface density of charge on the belt?

1. $6.7\times {10}^{-5}C{m}^{-2}$
2. $6.7\times {10}^{-7}C{m}^{-2}$
3. $6.7\times {10}^{-4}C{m}^{-2}$
4. $6.7\times {10}^{-8}C{m}^{-2}$

Q. Current in conductors is due to flow of positive charges.

1. True
2. False

Q. Two identical sized capacitors $C_1$ and $C_2$ are connected to a battery in series. A dielectric slab of dielectric constant $K=2$ is filled in the half region of both the capacitors as shown in figure.




$(C\to$ capacitance, $q\to$ charge stored, $U\to$ energy stored $)$

Match the following column:

Column I	Column II
$\left(A\right)$ $\frac{C_1}{C_2}$	$\left(p\right)$ $8/9$ $\left(q\right)$ $4/9$ $\left(r\right)$ $9/8$ $\left(s\right)$ None of these
$\left(B\right)$ $\frac{q_1}{q_2}$
$\left(C\right)$ $\frac{U_1}{U_2}$

1. $A\to r,B\to s,C\to p$
2. $A\to p,B\to r,C\to q$
3. $A\to r,B\to p,C\to s$
4. $A\to s,B\to s,C\to s$

Q. The current through a wire depends on time as $I=(2+3t)\text{A}$. Calculate the charge crossed through a cross-section of the wire in $10\text{s}$.

1. $17\text{C}$
2. $150\text{C}$
3. $20\text{C}$
4. $170\text{C}$

Q. Find the dimensions for electric power.

Q. Ram learned in high school that electric current is the flow of electrons. Ram’s teacher had also told him that at any temperature the electrons of any metal move very randomly with very high speeds (around 100km/second). So Ram imagines that when a current flows through a conductor, this random motion must cease and all electrons move in one particular direction like a marching army (flow in a sense)

1. Ram’s idea about motion of electrons is absolutely correct
2. Ram’s teacher had not told him the right idea about the motion of electrons at any temperature
3. What Ram learned In high school about current was wrong
4. Ram is drawing wrong conclusions because when current flows the random motion of electrons needn’t cease

Q. Two capacitors are connected in series as shown in figure. The equivalent capacitance between A and B is C₁. If a dielectric slab of dielectric constant ‘2’ is introduced completely in capacitor ‘C’, the equivalent capacitance between A and B now becomes C₂.
Find $\frac{C_1}{C_2}$.
दो संधारित्रों को चित्र में दर्शाए अनुसार श्रेणी में संयोजित किया जाता है। A तथा B के मध्‍य तुल्‍य धारिता C₁ है। यदि परावैद्युतांक ‘2’ की एक परावैद्युत पट्टिका को संधारित्र ‘C’ में पूर्णत: प्रवेशित किया जाता है, तब A तथा B के मध्‍य तुल्य धारिता C₂ हो जाती है।
$\frac{C_1}{C_2}$ ज्ञात कीजिए।

1. $\frac{3}{4}$
2. $\frac{3}{2}$
3. $\frac{2}{3}$
4. 1

Q. A source of emf $E=10\text{V}$ and having negligible internal resistance is connected to a variable resistance. The resistance varies as shown in figure. The total charge that has passed through the resistor $R$ during the time interval from $t_1$ to $t_2$ is

1. $40{\log }_{e}4$
2. $30{\log }_{e}3$
3. $20{\log }_{e}2$
4. $10{\log }_{e}2$

Q. The potential difference applied to an X-ray tube is 5 KV and the current through it is 3.2 mA. Then the number of electrons striking the target per second is

1. $2\times {10}^{16}$
2. $5\times {10}^6$
3. $1\times {10}^{17}$
4. $4\times {10}^{15}$

Q. In the Bohr’s model of hydrogen atom, the electrons moves around the nucleus in a circular orbit of a radius $5\times {10}^{-11}$ metre. It’s time period is $1.5\times {10}^{-16}$ sec. The current associated is

1. Zero
2. $1.6\times {10}^{-19}A$
3. $0.17A$
4. $1.07\times {10}^{-3}A$

Q. In an electrolyte $3.2\times {10}^{18}$ bivalent positive ions drift to the right per second while $3.6\times {10}^{18}$ monovalent negative ions drift to the left per second. Then the current is

1. 1.6 amp to the left
2. 1.6 amp to the right
3. 0.45 amp to the right
4. 0.45 amp to the left

Q. Two identical sized capacitors $C_1$ and $C_2$ are connected to a battery in series. A dielectric slab of dielectric constant $K=2$ is filled in the half region of both the capacitors as shown in figure.




$(C\to$ capacitance, $q\to$ charge stored, $U\to$ energy stored $)$

Match the following column:

Column I	Column II
$\left(A\right)$ $\frac{C_1}{C_2}$	$\left(p\right)$ $8/9$ $\left(q\right)$ $4/9$ $\left(r\right)$ $9/8$ $\left(s\right)$ None of these
$\left(B\right)$ $\frac{q_1}{q_2}$
$\left(C\right)$ $\frac{U_1}{U_2}$

1. $A\to s,B\to s,C\to s$
2. $A\to r,B\to p,C\to s$
3. $A\to p,B\to r,C\to q$
4. $A\to r,B\to s,C\to p$

Q. The current through a wire depends on time as $I=(2+3t)\text{A}$. Calculate the charge crossed through a cross-section of the wire in $10\text{s}$.

1. $150\text{C}$
2. $17\text{C}$
3. $20\text{C}$
4. $170\text{C}$

Q. The radius of an orbit of electron in hydrogen atom is $5\times {10}^{-11}m$. If the speed of electron is $2.2\times {10}^8$ m/s then the equivalent current due to orbital motion of electron is

1. 3.14 A
2. 11.2 A
3. 0.112 A
4. 0.01 A