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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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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 |
 53%
Level 3: 35%-60%
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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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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 |
 57%
Level 3: 35%-60%
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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 |
 51%
Level 3: 35%-60%
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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. \(900~\Omega\)
1. \(100~\Omega\)
2. \(200~\Omega\)
3. \(400~\Omega\)
4. \(900~\Omega\)
Subtopic: Â Kirchoff's Voltage Law |
 53%
Level 3: 35%-60%
Hints
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: Â Current & Current Density |
 51%
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%
Hints
\(n\) 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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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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