A beam of electrons emitted from the electron gun \(G\) is accelerated by an electric field \(E.\) The area of cross-section of the beam remains constant. As the beam moves away from \(G,\)
                   
(A) the speed of the electrons increases
(B) the current constituted by the beam increases
(C) the number of electrons per unit volume in the beam increases
(D) the number of electrons per unit volume in the beam decreases
Choose the correct option from the options given below:
1. (A), (B) and (C) only
2. (A) and (D) only
3. (B) and (D) only
4. (B), (C) and (D) only

Subtopic:  Current & Current Density |
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A cell with an EMF \(E\) and internal resistance \(r\) drives a current \(i\) through an external resistance \(R.\) The following statements describe the power and heat dissipation in the circuit:

(A) The cell supplies power equal to \(Ei.\)
(B) Heat is produced in \(R\) at the rate of \(Ei.\)
(C) Heat is produced in \(R\) at the rate of \(E i\bigg({\large\frac{R}{R+r}}\bigg).\)
(D) Heat is produced in the cell at the rate of \(E i\bigg({\large\frac{r}{R+r}}\bigg).\)

Choose the correct option from the options given below:

1. (A), (B) and (C) only
2. (A) and (B) only
3. (A) and (D) only
4. (A), (C) and (D) only
Subtopic:  Heating Effects of Current |
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A uniform metal wire of length \(l\) has \(10~\Omega \) resistance. Now this wire is stretched to a length \(2l\)  and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is:
1. \(10~\Omega \) 2. \(5~\Omega \)
3. \(40~\Omega \) 4. \(20~\Omega \)
Subtopic:  Current & Current Density |
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In the given circuit, what will be the current passing through the \(15 ~\Omega\) resistor?

1. \(\dfrac{3}{11}~\text{A}\)
2. \(\dfrac{4}{11}~\text{A}\)
3. \(\dfrac{5}{11}~\text{A}\)
4. zero
Subtopic:  Kirchoff's Current Law |
 51%
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In the circuit shown, current in 5 \(\Omega\) resistor is:
   
1. 1.5 A from Q to P
2. 1.5 A from P to Q
3. 3 A from P to Q
4. No current flows from Q to P
Subtopic:  Kirchoff's Voltage Law |
 66%
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Two wires A and B of equal lengths and of same metal are taken. The diameter of wire A is half to that of wire B. If the resistance of wire A is 48 \(\Omega\), then resistance of wire B is: 
1. 96 \(\Omega\)
2. 192 \(\Omega\)
3. 24 \(\Omega\)
4. 12 \(\Omega\)
Subtopic:  Derivation of Ohm's Law |
 59%
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\(n\) identical cells, each with an EMF \(E\) and internal resistance \(r,\) are connected in series to form a closed circuit. One of the cells, \(A,\) is connected with its polarity reversed. What is the potential difference across each cell (excluding cell \(A\))?
1. \(\dfrac{2E}{n}\) 2. \(\dfrac{E}{n}\)
3. \(\left(\dfrac{n-2}{n}\right)E\) 4. \(\left(\dfrac{2n}{n-2}\right)E\)
Subtopic:  Grouping of Cells |
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The current flowing through the resistance \(R_1\), when \(R_1=R_2\) and \(R_3=R_4\) is: 
               
1. \(\frac{V}{4\left(R_1+R_3\right)}\) 2. \(\frac{2 V}{\left(R_1+R_3\right)}\)
3. \(\frac{V}{\left(R_1+R_3\right)}\) 4. \(\frac{V}{2\left(R_1+R_3\right)}\)
Subtopic:  Current & Current Density |
 51%
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The resistance between \(A,B\) is found to be \(500~\Omega\)  while that between \(A,C\) is \(400~\Omega.\) The minimum possible value of \(R_2\) is:
             
1. \(100~\Omega\)
2. \(200~\Omega\)
3. \(400~\Omega\)
4. \(900~\Omega\)
Subtopic:  Kirchoff's Voltage Law |
 54%
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Nine similar resistors of resistance \(R\) are connected as shown in the figure. Equivalent resistance between points A and B is:
         
1. \(\frac{3}{5} R\)
2. \(\frac{4}{3} R\)
3. \(\frac{9}{5} R\)
4. \(R\)
Subtopic:  Combination of Resistors |
 53%
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