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Q. No.\(n\) 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: Â Grouping of Cells |
Level 4: Below 35%
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Current density is the current crossing per unit area. Consider a cylindrical wire of uniform cross-section \(A,\) carrying a current \(I.\) Imagine a cross-section formed by a "\(30^\circ\)-cut" as shown (the wire is not really cut). The current density perpendicular to this cross-section is:
| 1. | \(\dfrac{I}{A}\) | 2. | \(\dfrac{I}{A}~\cos30^\circ\) |
| 3. | \(\dfrac{2I}{A}\) | 4. | \(\dfrac{I}{A}~\sin30^\circ\) |
Subtopic: Â Current & Current Density |
Level 3: 35%-60%
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All the cells, shown in the figure below, are of \(2~\text V,\) and all the resistances are \(1~\Omega.\) When a potential difference \(V\) is applied between \(A\) and \(B,\) the current through the circuit doubles compared to the situation when the potential difference is made zero. Then;
| 1. | \(V=2\) volts, positive at \(A.\) |
| 2. | \(V=2\) volts, negative at \(A.\) |
| 3. | \(V=6\) volts, positive at \(A.\) |
| 4. | \(V=6\) volts, negative at \(A.\) |
Subtopic: Â Kirchoff's Voltage Law |
Level 3: 35%-60%
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Two wires \(A\) and \(B\) are made of the same metal and have equal lengths. The diameter of wire \(A\) is half the diameter of wire \(B.\) If the resistance of wire \(A\) is \(48~\Omega,\) the resistance of wire \(B\) will be:
| 1. | \(96~\Omega\) | 2. | \(192~\Omega\) |
| 3. | \(24~\Omega\) | 4. | \(12~\Omega\) |
Subtopic: Â Derivation of Ohm's Law |
 65%
Level 2: 60%+
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\(18\) cells each having the same EMF are connected in series with some cells being wrongly connected. This arrangement of battery is connected in series with an ammeter and two identical cells which are in series. Current of \(3~\text{A}\) is drawn when cells and battery support each other and current of \(2~\text{A}\) is drawn when cells and battery oppose each other. The number of wrongly connected cells is:
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(3\) | 4. | \(4\) |
Subtopic: Â Grouping of Cells |
Level 3: 35%-60%
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Two non-ideal batteries are connected in parallel: Battery of EMF \(E_1,\) resistance \(r_1\) and of EMF \(E_2\), resistance \(r_2.\) The resulting equivalent battery has EMF '\(E,\)' resistance \(r.\) If \(r_1<r_2,\)
1. \(|E-E_1|<|E-E_2|\)
2. \(|E+E_1|<|E+E_2|\)
3. \(|E-E_1|>|E-E_2|\)
4. \(|E+E_1|>|E+E_2|\)
1. \(|E-E_1|<|E-E_2|\)
2. \(|E+E_1|<|E+E_2|\)
3. \(|E-E_1|>|E-E_2|\)
4. \(|E+E_1|>|E+E_2|\)
Subtopic: Â Grouping of Cells |
Level 3: 35%-60%
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\(150\) cc of water taken in an electric kettle boils in \(20\) minutes. If the same amount of water is to be boiled in \(10\) minutes, the length of the heating element will have to be:
| 1. | one fourth | 2. | one third |
| 3. | two times | 4. | one half |
Subtopic: Â Heating Effects of Current |
Level 3: 35%-60%
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Each branch in the following circuit has a resistance \(R\).
The equivalent resistance of the circuit between points \(A\) and \(B\) is:
| 1. | \(R\) | 2. | \(2R\) |
| 3. | \(4R\) | 4. | \(8R\) |
Subtopic: Â Combination of Resistors |
Level 3: 35%-60%
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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 \(G,\)
Choose the correct option from the options given below:
| (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 |
| 1. | (A), (B) and (C) only |
| 2. | (A) and (D) only |
| 3. | (B) and (D) only |
| 4. | (B), (C) and (D) only |
Subtopic: Â Current & Current Density |
Level 3: 35%-60%
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Two hundred cells of the same emf \(E\) and same internal resistance \(r\) are connected in series in the same order without external resistance. The potential drop across \(50\) cells is found to be:
1. \(50E\)
2. \(150E\)
3. \(200E\)
4. zero
1. \(50E\)
2. \(150E\)
3. \(200E\)
4. zero
Subtopic: Â Grouping of Cells |
Level 3: 35%-60%
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