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Q. No.\(18\) 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 |
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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 |
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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 |
From NCERT
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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 |
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):
In the light of the above statements choose the correct answer from the options given below:
| Assertion (A): | Resistance of a conducting metallic wire depends on the voltage applied across it and current passing through it. |
| Reason (R): | Ohm's law is also valid for semiconductors. |
In the light of the above statements choose the correct answer from the options given below:
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | Both (A) and (R) are false. |
Subtopic: Â Derivation of Ohm's Law |
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The potential difference \(V_{AB}\) (in volts) is plotted as a function of the resistance \(R.\) The graph is given by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Derivation of Ohm's Law |
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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 |
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A thin circular conducting wire is connected at \(A,B\) where the smaller arc \(AB\) represents \(\dfrac14^{\text{th}}\) of the circumference. A current flows from \(A\) to \(B,\) dividing into two branches \(i_1\) and \(i_2\) at \(A.\) The ratio \(i_1:i_2\) equals:
| 1. | \(3\) | 2. | \(4\) |
| 3. | \(\dfrac13\) | 4. | \(1\) |
Subtopic: Â Combination of Resistors |
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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. \(R\)
1. \(\frac{3}{5} R\)
2. \(\frac{4}{3} R\)
3. \(\frac{9}{5} R\)
4. \(R\)
Subtopic: Â Combination of Resistors |
 53%
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The potential difference between the ends of a \(12~\text{V}\) battery when it is being charged by a \(2~\text{A}\) charger is found to be \(13.2~\text{V}\). If this battery is connected in a circuit with a \(6~\Omega\) resistance, the current will be nearly:
| 1. | \(2~\text{A}\) | 2. | \(1~\text{A}\) |
| 3. | \(1.8~\text{A}\) | 4. | \(2.2~\text{A}\) |
Subtopic: Â Kirchoff's Voltage Law |
 52%
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